[{"file_date_updated":"2021-08-11T12:44:16Z","title":"New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity","ec_funded":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2021-03-10T12:18:47Z","year":"2021","quality_controlled":"1","article_type":"original","oa":1,"citation":{"ista":"Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. 21(2), 291–323.","ama":"Izuchukwu C, Shehu Y. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. <i>Networks and Spatial Economics</i>. 2021;21(2):291-323. doi:<a href=\"https://doi.org/10.1007/s11067-021-09517-w\">10.1007/s11067-021-09517-w</a>","chicago":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” <i>Networks and Spatial Economics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11067-021-09517-w\">https://doi.org/10.1007/s11067-021-09517-w</a>.","apa":"Izuchukwu, C., &#38; Shehu, Y. (2021). New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. <i>Networks and Spatial Economics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11067-021-09517-w\">https://doi.org/10.1007/s11067-021-09517-w</a>","short":"C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323.","mla":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” <i>Networks and Spatial Economics</i>, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323, doi:<a href=\"https://doi.org/10.1007/s11067-021-09517-w\">10.1007/s11067-021-09517-w</a>.","ieee":"C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity,” <i>Networks and Spatial Economics</i>, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021."},"publication":"Networks and Spatial Economics","issue":"2","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","type":"journal_article","volume":21,"keyword":["Computer Networks and Communications","Software","Artificial Intelligence"],"day":"01","page":"291-323","publication_status":"published","file":[{"access_level":"open_access","file_id":"9884","checksum":"22b4253a2e5da843622a2df713784b4c","file_size":834964,"date_updated":"2021-08-11T12:44:16Z","success":1,"creator":"kschuh","date_created":"2021-08-11T12:44:16Z","file_name":"2021_NetworksSpatialEconomics_Shehu.pdf","relation":"main_file","content_type":"application/pdf"}],"_id":"9234","abstract":[{"lang":"eng","text":"In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps."}],"intvolume":"        21","status":"public","department":[{"_id":"VlKo"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"isi":1,"doi":"10.1007/s11067-021-09517-w","publication_identifier":{"eissn":["1572-9427"],"issn":["1566-113X"]},"license":"https://creativecommons.org/licenses/by/4.0/","acknowledgement":"The authors sincerely thank the Editor-in-Chief and anonymous referees for their careful reading, constructive comments and fruitful suggestions that help improve the manuscript. The research of the first author is supported by the National Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral Fellowship; Grant Number: 120784). The first author also acknowledges the financial support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Postdoctoral Fellowship. The second author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). Open Access funding provided by Institute of Science and Technology (IST Austria).","language":[{"iso":"eng"}],"external_id":{"isi":["000625002100001"]},"month":"06","oa_version":"Published Version","scopus_import":"1","has_accepted_license":"1","date_published":"2021-06-01T00:00:00Z","ddc":["510"],"author":[{"full_name":"Izuchukwu, Chinedu","last_name":"Izuchukwu","first_name":"Chinedu"},{"orcid":"0000-0001-9224-7139","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","full_name":"Shehu, Yekini"}],"date_updated":"2024-11-04T13:52:33Z","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications","corr_author":"1","quality_controlled":"1","article_type":"original","date_created":"2021-04-11T22:01:14Z","year":"2021","citation":{"short":"O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021).","ieee":"O. S. Iyiola and Y. Shehu, “New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications,” <i>Results in Mathematics</i>, vol. 76, no. 2. Springer Nature, 2021.","mla":"Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” <i>Results in Mathematics</i>, vol. 76, no. 2, 75, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00025-021-01381-x\">10.1007/s00025-021-01381-x</a>.","apa":"Iyiola, O. S., &#38; Shehu, Y. (2021). New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. <i>Results in Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00025-021-01381-x\">https://doi.org/10.1007/s00025-021-01381-x</a>","chicago":"Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” <i>Results in Mathematics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00025-021-01381-x\">https://doi.org/10.1007/s00025-021-01381-x</a>.","ama":"Iyiola OS, Shehu Y. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. <i>Results in Mathematics</i>. 2021;76(2). doi:<a href=\"https://doi.org/10.1007/s00025-021-01381-x\">10.1007/s00025-021-01381-x</a>","ista":"Iyiola OS, Shehu Y. 2021. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 76(2), 75."},"article_processing_charge":"No","issue":"2","publication":"Results in Mathematics","publisher":"Springer Nature","volume":76,"day":"25","type":"journal_article","publication_status":"published","_id":"9315","intvolume":"        76","abstract":[{"text":"We consider inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. To do these, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators in infinite dimensional real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature. We then show that Fermat–Weber location problem and primal–dual three-operator splitting are special cases of fixed point problem of nonexpansive mapping and consequently obtain the convergence analysis of inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. Some numerical implementations are drawn from primal–dual three-operator splitting to support the theoretical analysis.","lang":"eng"}],"status":"public","article_number":"75","department":[{"_id":"VlKo"}],"isi":1,"doi":"10.1007/s00025-021-01381-x","acknowledgement":"The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria.","publication_identifier":{"eissn":["1420-9012"],"issn":["1422-6383"]},"external_id":{"isi":["000632917700001"]},"language":[{"iso":"eng"}],"scopus_import":"1","oa_version":"None","month":"03","author":[{"last_name":"Iyiola","full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S."},{"full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","orcid":"0000-0001-9224-7139","first_name":"Yekini"}],"date_published":"2021-03-25T00:00:00Z","date_updated":"2024-10-09T21:00:33Z"},{"tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png"},"department":[{"_id":"GradSch"},{"_id":"VlKo"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","language":[{"iso":"eng"}],"conference":{"end_date":"2021-08-12","start_date":"2021-08-10","location":"Halifax, NS, Canada; Virtual","name":"CCCG: Canadian Conference on Computational Geometry"},"external_id":{"arxiv":["2106.11247"]},"month":"06","oa_version":"Published Version","has_accepted_license":"1","date_published":"2021-06-29T00:00:00Z","ddc":["516"],"author":[{"id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin","last_name":"Dvorak","orcid":"0000-0001-5293-214X","first_name":"Martin"},{"first_name":"Sara","last_name":"Nicholson","full_name":"Nicholson, Sara"}],"date_updated":"2025-05-14T11:23:45Z","file_date_updated":"2021-08-12T10:57:21Z","title":"Massively winning configurations in the convex grabbing game on the plane","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2021-06-22T15:57:11Z","year":"2021","quality_controlled":"1","oa":1,"citation":{"short":"M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2021.","mla":"Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” <i>Proceedings of the 33rd Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2021.","ieee":"M. Dvorak and S. Nicholson, “Massively winning configurations in the convex grabbing game on the plane,” in <i>Proceedings of the 33rd Canadian Conference on Computational Geometry</i>, Halifax, NS, Canada; Virtual, 2021.","apa":"Dvorak, M., &#38; Nicholson, S. (2021). Massively winning configurations in the convex grabbing game on the plane. In <i>Proceedings of the 33rd Canadian Conference on Computational Geometry</i>. Halifax, NS, Canada; Virtual: Canadian Conference on Computational Geometry.","chicago":"Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” In <i>Proceedings of the 33rd Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry, 2021.","ama":"Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. In: <i>Proceedings of the 33rd Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2021.","ista":"Dvorak M, Nicholson S. 2021. Massively winning configurations in the convex grabbing game on the plane. Proceedings of the 33rd Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry."},"publication":"Proceedings of the 33rd Canadian Conference on Computational Geometry","publisher":"Canadian Conference on Computational Geometry","article_processing_charge":"No","type":"conference","keyword":["convex grabbing game","graph grabbing game","combinatorial game","convex geometry"],"day":"29","arxiv":1,"publication_status":"published","file":[{"checksum":"45accb1de9b7e0e4bb2fbfe5fd3e6239","file_size":381306,"file_id":"9616","access_level":"open_access","content_type":"application/pdf","relation":"main_file","date_created":"2021-06-28T20:23:13Z","file_name":"Convex-Grabbing-Game_CCCG_proc_version.pdf","success":1,"creator":"mdvorak","date_updated":"2021-06-28T20:23:13Z"},{"access_level":"open_access","file_id":"9902","checksum":"9199cf18c65658553487458cc24d0ab2","file_size":403645,"date_updated":"2021-08-12T10:57:21Z","creator":"kschuh","success":1,"file_name":"Convex-Grabbing-Game_FULL-VERSION.pdf","date_created":"2021-08-12T10:57:21Z","relation":"main_file","content_type":"application/pdf"}],"_id":"9592","abstract":[{"text":"The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large odd-sized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large even-sized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general.","lang":"eng"}],"status":"public"},{"scopus_import":"1","oa_version":"Submitted Version","has_accepted_license":"1","month":"11","external_id":{"isi":["000564648400018"]},"language":[{"iso":"eng"}],"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"date_updated":"2024-11-04T13:52:37Z","author":[{"orcid":"0000-0001-9224-7139","first_name":"Yekini","full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu"},{"first_name":"Olaniyi S.","last_name":"Iyiola","full_name":"Iyiola, Olaniyi S."}],"date_published":"2020-11-01T00:00:00Z","ddc":["510"],"isi":1,"department":[{"_id":"VlKo"}],"acknowledgement":"The authors are grateful to the two anonymous referees for their insightful comments and suggestions which have improved the earlier version of the manuscript greatly. The first author has received funding from the European Research Council (ERC) under the European Union Seventh Framework Programme (FP7 - 2007-2013) (Grant agreement No. 616160).","publication_identifier":{"issn":["0168-9274"]},"doi":"10.1016/j.apnum.2020.06.009","volume":157,"page":"315-337","day":"01","type":"journal_article","article_processing_charge":"No","publication":"Applied Numerical Mathematics","publisher":"Elsevier","_id":"8077","abstract":[{"text":"The projection methods with vanilla inertial extrapolation step for variational inequalities have been of interest to many authors recently due to the improved convergence speed contributed by the presence of inertial extrapolation step. However, it is discovered that these projection methods with inertial steps lose the Fejér monotonicity of the iterates with respect to the solution, which is being enjoyed by their corresponding non-inertial projection methods for variational inequalities. This lack of Fejér monotonicity makes projection methods with vanilla inertial extrapolation step for variational inequalities not to converge faster than their corresponding non-inertial projection methods at times. Also, it has recently been proved that the projection methods with vanilla inertial extrapolation step may provide convergence rates that are worse than the classical projected gradient methods for strongly convex functions. In this paper, we introduce projection methods with alternated inertial extrapolation step for solving variational inequalities. We show that the sequence of iterates generated by our methods converges weakly to a solution of the variational inequality under some appropriate conditions. The Fejér monotonicity of even subsequence is recovered in these methods and linear rate of convergence is obtained. The numerical implementations of our methods compared with some other inertial projection methods show that our method is more efficient and outperforms some of these inertial projection methods.","lang":"eng"}],"intvolume":"       157","status":"public","publication_status":"published","file":[{"relation":"main_file","content_type":"application/pdf","date_created":"2020-07-02T09:08:59Z","file_name":"2020_AppliedNumericalMath_Shehu.pdf","creator":"dernst","date_updated":"2020-07-14T12:48:09Z","checksum":"87d81324a62c82baa925c009dfcb0200","file_size":2874203,"file_id":"8078","access_level":"open_access"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2020-07-14T12:48:09Z","title":"Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence","ec_funded":1,"citation":{"chicago":"Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” <i>Applied Numerical Mathematics</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.apnum.2020.06.009\">https://doi.org/10.1016/j.apnum.2020.06.009</a>.","apa":"Shehu, Y., &#38; Iyiola, O. S. (2020). Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. <i>Applied Numerical Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.apnum.2020.06.009\">https://doi.org/10.1016/j.apnum.2020.06.009</a>","ista":"Shehu Y, Iyiola OS. 2020. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. 157, 315–337.","ama":"Shehu Y, Iyiola OS. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. <i>Applied Numerical Mathematics</i>. 2020;157:315-337. doi:<a href=\"https://doi.org/10.1016/j.apnum.2020.06.009\">10.1016/j.apnum.2020.06.009</a>","ieee":"Y. Shehu and O. S. Iyiola, “Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence,” <i>Applied Numerical Mathematics</i>, vol. 157. Elsevier, pp. 315–337, 2020.","short":"Y. Shehu, O.S. Iyiola, Applied Numerical Mathematics 157 (2020) 315–337.","mla":"Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” <i>Applied Numerical Mathematics</i>, vol. 157, Elsevier, 2020, pp. 315–37, doi:<a href=\"https://doi.org/10.1016/j.apnum.2020.06.009\">10.1016/j.apnum.2020.06.009</a>."},"oa":1,"quality_controlled":"1","corr_author":"1","article_type":"original","date_created":"2020-07-02T09:02:33Z","year":"2020"},{"acknowledgement":"The research of this author is supported by the ERC grant at the IST.","publication_identifier":{"issn":["1017-1398"],"eissn":["1572-9265"]},"doi":"10.1007/s11075-019-00758-y","isi":1,"department":[{"_id":"VlKo"}],"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"date_updated":"2024-11-04T13:52:40Z","author":[{"last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","first_name":"Yekini"},{"first_name":"Xiao-Huan","last_name":"Li","full_name":"Li, Xiao-Huan"},{"first_name":"Qiao-Li","last_name":"Dong","full_name":"Dong, Qiao-Li"}],"date_published":"2020-05-01T00:00:00Z","ddc":["000"],"scopus_import":"1","oa_version":"Submitted Version","has_accepted_license":"1","month":"05","external_id":{"isi":["000528979000015"]},"language":[{"iso":"eng"}],"citation":{"ama":"Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. <i>Numerical Algorithms</i>. 2020;84:365-388. doi:<a href=\"https://doi.org/10.1007/s11075-019-00758-y\">10.1007/s11075-019-00758-y</a>","ista":"Shehu Y, Li X-H, Dong Q-L. 2020. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 84, 365–388.","apa":"Shehu, Y., Li, X.-H., &#38; Dong, Q.-L. (2020). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. <i>Numerical Algorithms</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11075-019-00758-y\">https://doi.org/10.1007/s11075-019-00758-y</a>","chicago":"Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” <i>Numerical Algorithms</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11075-019-00758-y\">https://doi.org/10.1007/s11075-019-00758-y</a>.","ieee":"Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for monotone variational inequalities in Hilbert spaces,” <i>Numerical Algorithms</i>, vol. 84. Springer Nature, pp. 365–388, 2020.","short":"Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.","mla":"Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” <i>Numerical Algorithms</i>, vol. 84, Springer Nature, 2020, pp. 365–88, doi:<a href=\"https://doi.org/10.1007/s11075-019-00758-y\">10.1007/s11075-019-00758-y</a>."},"oa":1,"quality_controlled":"1","corr_author":"1","article_type":"original","date_created":"2019-06-27T20:09:33Z","year":"2020","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2020-07-14T12:47:34Z","title":"An efficient projection-type method for monotone variational inequalities in Hilbert spaces","ec_funded":1,"_id":"6593","abstract":[{"lang":"eng","text":"We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising."}],"intvolume":"        84","status":"public","publication_status":"published","file":[{"relation":"main_file","content_type":"application/pdf","file_name":"ExtragradientMethodPaper.pdf","date_created":"2019-10-01T13:14:10Z","creator":"kschuh","date_updated":"2020-07-14T12:47:34Z","file_size":359654,"checksum":"bb1a1eb3ebb2df380863d0db594673ba","file_id":"6927","access_level":"open_access"}],"volume":84,"page":"365-388","day":"01","type":"journal_article","article_processing_charge":"No","publication":"Numerical Algorithms","publisher":"Springer Nature"},{"month":"03","scopus_import":"1","oa_version":"Submitted Version","has_accepted_license":"1","language":[{"iso":"eng"}],"external_id":{"isi":["000511805200009"]},"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160"}],"date_updated":"2024-11-04T13:52:44Z","date_published":"2020-03-01T00:00:00Z","ddc":["518","510","515"],"author":[{"full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini","orcid":"0000-0001-9224-7139"},{"full_name":"Gibali, Aviv","last_name":"Gibali","first_name":"Aviv"},{"last_name":"Sagratella","full_name":"Sagratella, Simone","first_name":"Simone"}],"isi":1,"department":[{"_id":"VlKo"}],"publication_identifier":{"eissn":["1573-2878"],"issn":["0022-3239"]},"acknowledgement":"We are grateful to the anonymous referees and editor whose insightful comments helped to considerably improve an earlier version of this paper. The research of the first author is supported by an ERC Grant from the Institute of Science and Technology (IST).","doi":"10.1007/s10957-019-01616-6","type":"journal_article","volume":184,"page":"877–894","day":"01","publication":"Journal of Optimization Theory and Applications","publisher":"Springer Nature","article_processing_charge":"No","_id":"7161","abstract":[{"lang":"eng","text":"In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature."}],"intvolume":"       184","status":"public","publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","file_name":"2020_JourOptimizationTheoryApplic_Shehu.pdf","date_created":"2020-10-12T10:40:27Z","creator":"dernst","embargo":"2021-03-15","date_updated":"2021-03-16T23:30:04Z","file_size":332641,"checksum":"9f6dc6c6bf2b48cb3a2091a9ed5feaf2","file_id":"8647","access_level":"open_access"}],"file_date_updated":"2021-03-16T23:30:04Z","ec_funded":1,"title":"Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"citation":{"ieee":"Y. Shehu, A. Gibali, and S. Sagratella, “Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces,” <i>Journal of Optimization Theory and Applications</i>, vol. 184. Springer Nature, pp. 877–894, 2020.","mla":"Shehu, Yekini, et al. “Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” <i>Journal of Optimization Theory and Applications</i>, vol. 184, Springer Nature, 2020, pp. 877–894, doi:<a href=\"https://doi.org/10.1007/s10957-019-01616-6\">10.1007/s10957-019-01616-6</a>.","short":"Y. Shehu, A. Gibali, S. Sagratella, Journal of Optimization Theory and Applications 184 (2020) 877–894.","ama":"Shehu Y, Gibali A, Sagratella S. Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. <i>Journal of Optimization Theory and Applications</i>. 2020;184:877–894. doi:<a href=\"https://doi.org/10.1007/s10957-019-01616-6\">10.1007/s10957-019-01616-6</a>","ista":"Shehu Y, Gibali A, Sagratella S. 2020. Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. 184, 877–894.","apa":"Shehu, Y., Gibali, A., &#38; Sagratella, S. (2020). Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. <i>Journal of Optimization Theory and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10957-019-01616-6\">https://doi.org/10.1007/s10957-019-01616-6</a>","chicago":"Shehu, Yekini, Aviv Gibali, and Simone Sagratella. “Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” <i>Journal of Optimization Theory and Applications</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10957-019-01616-6\">https://doi.org/10.1007/s10957-019-01616-6</a>."},"date_created":"2019-12-09T21:33:44Z","year":"2020","quality_controlled":"1","article_type":"original"},{"article_number":"138","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"department":[{"_id":"VlKo"}],"isi":1,"doi":"10.1007/s00025-019-1061-4","publication_identifier":{"issn":["1422-6383"],"eissn":["1420-9012"]},"external_id":{"arxiv":["2101.09068"],"isi":["000473237500002"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","oa_version":"Published Version","scopus_import":"1","month":"12","author":[{"orcid":"0000-0001-9224-7139","first_name":"Yekini","last_name":"Shehu","full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"}],"ddc":["000"],"date_published":"2019-12-01T00:00:00Z","date_updated":"2024-11-04T13:52:40Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces","ec_funded":1,"file_date_updated":"2020-07-14T12:47:34Z","article_type":"original","corr_author":"1","quality_controlled":"1","year":"2019","date_created":"2019-06-29T10:11:30Z","citation":{"ama":"Shehu Y. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. <i>Results in Mathematics</i>. 2019;74(4). doi:<a href=\"https://doi.org/10.1007/s00025-019-1061-4\">10.1007/s00025-019-1061-4</a>","ista":"Shehu Y. 2019. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138.","apa":"Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. <i>Results in Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s00025-019-1061-4\">https://doi.org/10.1007/s00025-019-1061-4</a>","chicago":"Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” <i>Results in Mathematics</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00025-019-1061-4\">https://doi.org/10.1007/s00025-019-1061-4</a>.","ieee":"Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces,” <i>Results in Mathematics</i>, vol. 74, no. 4. Springer, 2019.","short":"Y. Shehu, Results in Mathematics 74 (2019).","mla":"Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” <i>Results in Mathematics</i>, vol. 74, no. 4, 138, Springer, 2019, doi:<a href=\"https://doi.org/10.1007/s00025-019-1061-4\">10.1007/s00025-019-1061-4</a>."},"oa":1,"article_processing_charge":"Yes (via OA deal)","publisher":"Springer","issue":"4","publication":"Results in Mathematics","day":"01","volume":74,"type":"journal_article","file":[{"creator":"kschuh","date_updated":"2020-07-14T12:47:34Z","relation":"main_file","content_type":"application/pdf","file_name":"Springer_2019_Shehu.pdf","date_created":"2019-07-03T15:20:40Z","file_id":"6605","access_level":"open_access","checksum":"c6d18cb1e16fc0c36a0e0f30b4ebbc2d","file_size":466942}],"publication_status":"published","arxiv":1,"status":"public","_id":"6596","intvolume":"        74","abstract":[{"lang":"eng","text":"It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper."}]},{"year":"2019","date_created":"2019-07-29T12:23:29Z","quality_controlled":"1","oa":1,"citation":{"ieee":"V. Kolmogorov, “Testing the complexity of a valued CSP language,” in <i>46th International Colloquium on Automata, Languages and Programming</i>, Patras, Greece, 2019, vol. 132, p. 77:1-77:12.","mla":"Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” <i>46th International Colloquium on Automata, Languages and Programming</i>, vol. 132, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12, doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">10.4230/LIPICS.ICALP.2019.77</a>.","short":"V. Kolmogorov, in:, 46th International Colloquium on Automata, Languages and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12.","ama":"Kolmogorov V. Testing the complexity of a valued CSP language. In: <i>46th International Colloquium on Automata, Languages and Programming</i>. Vol 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:77:1-77:12. doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">10.4230/LIPICS.ICALP.2019.77</a>","ista":"Kolmogorov V. 2019. Testing the complexity of a valued CSP language. 46th International Colloquium on Automata, Languages and Programming. ICALP: Automata, Languages and Programming, LIPIcs, vol. 132, 77:1-77:12.","apa":"Kolmogorov, V. (2019). Testing the complexity of a valued CSP language. In <i>46th International Colloquium on Automata, Languages and Programming</i> (Vol. 132, p. 77:1-77:12). Patras, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">https://doi.org/10.4230/LIPICS.ICALP.2019.77</a>","chicago":"Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” In <i>46th International Colloquium on Automata, Languages and Programming</i>, 132:77:1-77:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.77\">https://doi.org/10.4230/LIPICS.ICALP.2019.77</a>."},"ec_funded":1,"title":"Testing the complexity of a valued CSP language","file_date_updated":"2020-07-14T12:47:38Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"file":[{"date_updated":"2020-07-14T12:47:38Z","creator":"dernst","date_created":"2019-07-31T07:01:45Z","file_name":"2019_LIPICS_Kolmogorov.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_id":"6738","checksum":"f5ebee8eec6ae09e30365578ee63a492","file_size":575475}],"publication_status":"published","status":"public","_id":"6725","abstract":[{"lang":"eng","text":"A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language. \r\nRecent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds."}],"intvolume":"       132","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication":"46th International Colloquium on Automata, Languages and Programming","article_processing_charge":"No","type":"conference","page":"77:1-77:12","day":"01","volume":132,"doi":"10.4230/LIPICS.ICALP.2019.77","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-109-2"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"department":[{"_id":"VlKo"}],"alternative_title":["LIPIcs"],"ddc":["000"],"date_published":"2019-07-01T00:00:00Z","author":[{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"}],"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"date_updated":"2025-07-10T11:53:47Z","conference":{"name":"ICALP: Automata, Languages and Programming","location":"Patras, Greece","start_date":"2019-07-08","end_date":"2019-07-12"},"language":[{"iso":"eng"}],"external_id":{"arxiv":["1803.02289"]},"month":"07","has_accepted_license":"1","scopus_import":"1","oa_version":"Published Version"},{"month":"12","oa_version":"Published Version","scopus_import":"1","has_accepted_license":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2101.09081"],"isi":["000488973100005"]},"date_updated":"2024-11-04T13:52:44Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160"}],"date_published":"2019-12-01T00:00:00Z","ddc":["510","515","518"],"author":[{"full_name":"Shehu, Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","first_name":"Yekini"},{"first_name":"Olaniyi S.","last_name":"Iyiola","full_name":"Iyiola, Olaniyi S."},{"full_name":"Li, Xiao-Huan","last_name":"Li","first_name":"Xiao-Huan"},{"first_name":"Qiao-Li","last_name":"Dong","full_name":"Dong, Qiao-Li"}],"isi":1,"department":[{"_id":"VlKo"}],"article_number":"161","publication_identifier":{"issn":["2238-3603"],"eissn":["1807-0302"]},"doi":"10.1007/s40314-019-0955-9","type":"journal_article","volume":38,"day":"01","issue":"4","publication":"Computational and Applied Mathematics","publisher":"Springer Nature","article_processing_charge":"No","intvolume":"        38","_id":"7000","abstract":[{"text":"The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps.","lang":"eng"}],"status":"public","main_file_link":[{"url":"https://doi.org/10.1007/s40314-019-0955-9","open_access":"1"}],"arxiv":1,"publication_status":"published","title":"Convergence analysis of projection method for variational inequalities","ec_funded":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"citation":{"ieee":"Y. Shehu, O. S. Iyiola, X.-H. Li, and Q.-L. Dong, “Convergence analysis of projection method for variational inequalities,” <i>Computational and Applied Mathematics</i>, vol. 38, no. 4. Springer Nature, 2019.","short":"Y. Shehu, O.S. Iyiola, X.-H. Li, Q.-L. Dong, Computational and Applied Mathematics 38 (2019).","mla":"Shehu, Yekini, et al. “Convergence Analysis of Projection Method for Variational Inequalities.” <i>Computational and Applied Mathematics</i>, vol. 38, no. 4, 161, Springer Nature, 2019, doi:<a href=\"https://doi.org/10.1007/s40314-019-0955-9\">10.1007/s40314-019-0955-9</a>.","chicago":"Shehu, Yekini, Olaniyi S. Iyiola, Xiao-Huan Li, and Qiao-Li Dong. “Convergence Analysis of Projection Method for Variational Inequalities.” <i>Computational and Applied Mathematics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s40314-019-0955-9\">https://doi.org/10.1007/s40314-019-0955-9</a>.","apa":"Shehu, Y., Iyiola, O. S., Li, X.-H., &#38; Dong, Q.-L. (2019). Convergence analysis of projection method for variational inequalities. <i>Computational and Applied Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40314-019-0955-9\">https://doi.org/10.1007/s40314-019-0955-9</a>","ista":"Shehu Y, Iyiola OS, Li X-H, Dong Q-L. 2019. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 38(4), 161.","ama":"Shehu Y, Iyiola OS, Li X-H, Dong Q-L. Convergence analysis of projection method for variational inequalities. <i>Computational and Applied Mathematics</i>. 2019;38(4). doi:<a href=\"https://doi.org/10.1007/s40314-019-0955-9\">10.1007/s40314-019-0955-9</a>"},"date_created":"2019-11-12T12:41:44Z","year":"2019","corr_author":"1","quality_controlled":"1","article_type":"original"},{"date_updated":"2024-11-04T13:52:36Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"}],"author":[{"first_name":"Dimitris","last_name":"Achlioptas","full_name":"Achlioptas, Dimitris"},{"last_name":"Iliopoulos","full_name":"Iliopoulos, Fotis","first_name":"Fotis"},{"last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir"}],"date_published":"2019-10-31T00:00:00Z","oa_version":"Preprint","scopus_import":"1","month":"10","external_id":{"isi":["000493900200005"],"arxiv":["1809.01537"]},"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"doi":"10.1137/16m109332x","department":[{"_id":"VlKo"}],"isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1809.01537","open_access":"1"}],"status":"public","abstract":[{"lang":"eng","text":"We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These algorithms search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a random nearby state that addresses the violation, while (we hope) not introducing many new violations. An important class of focused local search algorithms with provable performance guarantees has recently arisen from algorithmizations of the Lovász local lemma (LLL), a nonconstructive tool for proving the existence of satisfying states by introducing a background measure on the state space. While powerful, the state transitions of algorithms in this class must be, in a precise sense, perfectly compatible with the background measure. In many applications this is a very restrictive requirement, and one needs to step outside the class. Here we introduce the notion of measure distortion and develop a framework for analyzing arbitrary focused stochastic local search algorithms, recovering LLL algorithmizations as the special case of no distortion. Our framework takes as input an arbitrary algorithm of such type and an arbitrary probability measure and shows how to use the measure as a yardstick of algorithmic progress, even for algorithms designed independently of the measure."}],"_id":"7412","intvolume":"        48","publication_status":"published","arxiv":1,"day":"31","page":"1583-1602","volume":48,"type":"journal_article","article_processing_charge":"No","publisher":"SIAM","publication":"SIAM Journal on Computing","issue":"5","citation":{"apa":"Achlioptas, D., Iliopoulos, F., &#38; Kolmogorov, V. (2019). A local lemma for focused stochastical algorithms. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/16m109332x\">https://doi.org/10.1137/16m109332x</a>","chicago":"Achlioptas, Dimitris, Fotis Iliopoulos, and Vladimir Kolmogorov. “A Local Lemma for Focused Stochastical Algorithms.” <i>SIAM Journal on Computing</i>. SIAM, 2019. <a href=\"https://doi.org/10.1137/16m109332x\">https://doi.org/10.1137/16m109332x</a>.","ama":"Achlioptas D, Iliopoulos F, Kolmogorov V. A local lemma for focused stochastical algorithms. <i>SIAM Journal on Computing</i>. 2019;48(5):1583-1602. doi:<a href=\"https://doi.org/10.1137/16m109332x\">10.1137/16m109332x</a>","ista":"Achlioptas D, Iliopoulos F, Kolmogorov V. 2019. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 48(5), 1583–1602.","mla":"Achlioptas, Dimitris, et al. “A Local Lemma for Focused Stochastical Algorithms.” <i>SIAM Journal on Computing</i>, vol. 48, no. 5, SIAM, 2019, pp. 1583–602, doi:<a href=\"https://doi.org/10.1137/16m109332x\">10.1137/16m109332x</a>.","short":"D. Achlioptas, F. Iliopoulos, V. Kolmogorov, SIAM Journal on Computing 48 (2019) 1583–1602.","ieee":"D. Achlioptas, F. Iliopoulos, and V. Kolmogorov, “A local lemma for focused stochastical algorithms,” <i>SIAM Journal on Computing</i>, vol. 48, no. 5. SIAM, pp. 1583–1602, 2019."},"oa":1,"article_type":"original","quality_controlled":"1","year":"2019","date_created":"2020-01-30T09:27:32Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ec_funded":1,"title":"A local lemma for focused stochastical algorithms"},{"publication_identifier":{"issn":["1063-6919"],"isbn":["9781728132938"]},"doi":"10.1109/CVPR.2019.01140","department":[{"_id":"VlKo"}],"isi":1,"article_number":"11138-11147","date_updated":"2025-07-10T11:54:39Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160"}],"date_published":"2019-06-01T00:00:00Z","author":[{"first_name":"Paul","last_name":"Swoboda","full_name":"Swoboda, Paul","id":"446560C6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"}],"month":"06","oa_version":"Preprint","scopus_import":"1","conference":{"start_date":"2019-06-15","end_date":"2019-06-20","name":"CVPR: Conference on Computer Vision and Pattern Recognition","location":"Long Beach, CA, United States"},"language":[{"iso":"eng"}],"external_id":{"isi":["000542649304076"],"arxiv":["1806.05049"]},"oa":1,"citation":{"ieee":"P. Swoboda and V. Kolmogorov, “Map inference via block-coordinate Frank-Wolfe algorithm,” in <i>Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>, Long Beach, CA, United States, 2019, vol. 2019–June.","short":"P. Swoboda, V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2019.","mla":"Swoboda, Paul, and Vladimir Kolmogorov. “Map Inference via Block-Coordinate Frank-Wolfe Algorithm.” <i>Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>, vol. 2019–June, 11138–11147, IEEE, 2019, doi:<a href=\"https://doi.org/10.1109/CVPR.2019.01140\">10.1109/CVPR.2019.01140</a>.","chicago":"Swoboda, Paul, and Vladimir Kolmogorov. “Map Inference via Block-Coordinate Frank-Wolfe Algorithm.” In <i>Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>, Vol. 2019–June. IEEE, 2019. <a href=\"https://doi.org/10.1109/CVPR.2019.01140\">https://doi.org/10.1109/CVPR.2019.01140</a>.","apa":"Swoboda, P., &#38; Kolmogorov, V. (2019). Map inference via block-coordinate Frank-Wolfe algorithm. In <i>Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i> (Vol. 2019–June). Long Beach, CA, United States: IEEE. <a href=\"https://doi.org/10.1109/CVPR.2019.01140\">https://doi.org/10.1109/CVPR.2019.01140</a>","ista":"Swoboda P, Kolmogorov V. 2019. Map inference via block-coordinate Frank-Wolfe algorithm. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition vol. 2019–June, 11138–11147.","ama":"Swoboda P, Kolmogorov V. Map inference via block-coordinate Frank-Wolfe algorithm. In: <i>Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>. Vol 2019-June. IEEE; 2019. doi:<a href=\"https://doi.org/10.1109/CVPR.2019.01140\">10.1109/CVPR.2019.01140</a>"},"year":"2019","date_created":"2020-02-09T23:00:52Z","quality_controlled":"1","title":"Map inference via block-coordinate Frank-Wolfe algorithm","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","abstract":[{"text":"We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane block-coordinate Frank-Wolfe method that takes advantage of the specific structure of the Lagrangean decomposition. We show empirically that our method outperforms state-of-the-art Lagrangean decomposition based algorithms on some challenging Markov Random Field, multi-label discrete tomography and graph matching problems.","lang":"eng"}],"_id":"7468","main_file_link":[{"url":"https://arxiv.org/abs/1806.05049","open_access":"1"}],"arxiv":1,"publication_status":"published","type":"conference","day":"01","volume":"2019-June","publisher":"IEEE","publication":"Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition","article_processing_charge":"No"},{"article_processing_charge":"No","external_id":{"isi":["000554591600090"]},"conference":{"location":"Seoul, South Korea","name":"ICCVW: International Conference on Computer Vision Workshop","end_date":"2019-10-28","start_date":"2019-10-27"},"publisher":"IEEE","publication":"Proceedings of the 2019 International Conference on Computer Vision Workshop","language":[{"iso":"eng"}],"day":"01","scopus_import":"1","oa_version":"None","type":"conference","month":"10","author":[{"last_name":"Rannen-Triki","full_name":"Rannen-Triki, Amal","first_name":"Amal"},{"full_name":"Berman, Maxim","last_name":"Berman","first_name":"Maxim"},{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"first_name":"Matthew B.","full_name":"Blaschko, Matthew B.","last_name":"Blaschko"}],"publication_status":"published","date_published":"2019-10-01T00:00:00Z","status":"public","date_updated":"2023-09-08T11:19:12Z","abstract":[{"text":"Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of functions defined by a network and the difficulty in measuring function complexity. There exists no method in the literature for additive regularization based on a norm of the function, as is classically considered in statistical learning theory. In this work, we study the tractability of function norms for deep neural networks with ReLU activations. We provide, to the best of our knowledge, the first proof in the literature of the NP-hardness of computing function norms of DNNs of 3 or more layers. We also highlight a fundamental difference between shallow and deep networks. In the light on these results, we propose a new regularization strategy based on approximate function norms, and show its efficiency on a segmentation task with a DNN.","lang":"eng"}],"_id":"7639","article_number":"748-752","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","isi":1,"department":[{"_id":"VlKo"}],"title":"Function norms for neural networks","quality_controlled":"1","year":"2019","date_created":"2020-04-05T22:00:50Z","doi":"10.1109/ICCVW.2019.00097","citation":{"mla":"Rannen-Triki, Amal, et al. “Function Norms for Neural Networks.” <i>Proceedings of the 2019 International Conference on Computer Vision Workshop</i>, 748–752, IEEE, 2019, doi:<a href=\"https://doi.org/10.1109/ICCVW.2019.00097\">10.1109/ICCVW.2019.00097</a>.","short":"A. Rannen-Triki, M. Berman, V. Kolmogorov, M.B. Blaschko, in:, Proceedings of the 2019 International Conference on Computer Vision Workshop, IEEE, 2019.","ieee":"A. Rannen-Triki, M. Berman, V. Kolmogorov, and M. B. Blaschko, “Function norms for neural networks,” in <i>Proceedings of the 2019 International Conference on Computer Vision Workshop</i>, Seoul, South Korea, 2019.","ista":"Rannen-Triki A, Berman M, Kolmogorov V, Blaschko MB. 2019. Function norms for neural networks. Proceedings of the 2019 International Conference on Computer Vision Workshop. ICCVW: International Conference on Computer Vision Workshop, 748–752.","ama":"Rannen-Triki A, Berman M, Kolmogorov V, Blaschko MB. Function norms for neural networks. In: <i>Proceedings of the 2019 International Conference on Computer Vision Workshop</i>. IEEE; 2019. doi:<a href=\"https://doi.org/10.1109/ICCVW.2019.00097\">10.1109/ICCVW.2019.00097</a>","chicago":"Rannen-Triki, Amal, Maxim Berman, Vladimir Kolmogorov, and Matthew B. Blaschko. “Function Norms for Neural Networks.” In <i>Proceedings of the 2019 International Conference on Computer Vision Workshop</i>. IEEE, 2019. <a href=\"https://doi.org/10.1109/ICCVW.2019.00097\">https://doi.org/10.1109/ICCVW.2019.00097</a>.","apa":"Rannen-Triki, A., Berman, M., Kolmogorov, V., &#38; Blaschko, M. B. (2019). Function norms for neural networks. In <i>Proceedings of the 2019 International Conference on Computer Vision Workshop</i>. Seoul, South Korea: IEEE. <a href=\"https://doi.org/10.1109/ICCVW.2019.00097\">https://doi.org/10.1109/ICCVW.2019.00097</a>"},"publication_identifier":{"isbn":["9781728150239"]}},{"citation":{"ista":"Mohapatra P, Rolinek M, Jawahar CV, Kolmogorov V, Kumar MP. 2018. Efficient optimization for rank-based loss functions. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition, 3693–3701.","ama":"Mohapatra P, Rolinek M, Jawahar CV, Kolmogorov V, Kumar MP. Efficient optimization for rank-based loss functions. In: <i>2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition</i>. IEEE; 2018:3693-3701. doi:<a href=\"https://doi.org/10.1109/cvpr.2018.00389\">10.1109/cvpr.2018.00389</a>","chicago":"Mohapatra, Pritish, Michal Rolinek, C V Jawahar, Vladimir Kolmogorov, and M Pawan Kumar. “Efficient Optimization for Rank-Based Loss Functions.” In <i>2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition</i>, 3693–3701. IEEE, 2018. <a href=\"https://doi.org/10.1109/cvpr.2018.00389\">https://doi.org/10.1109/cvpr.2018.00389</a>.","apa":"Mohapatra, P., Rolinek, M., Jawahar, C. V., Kolmogorov, V., &#38; Kumar, M. P. (2018). Efficient optimization for rank-based loss functions. In <i>2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition</i> (pp. 3693–3701). Salt Lake City, UT, USA: IEEE. <a href=\"https://doi.org/10.1109/cvpr.2018.00389\">https://doi.org/10.1109/cvpr.2018.00389</a>","short":"P. Mohapatra, M. Rolinek, C.V. Jawahar, V. Kolmogorov, M.P. Kumar, in:, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, IEEE, 2018, pp. 3693–3701.","mla":"Mohapatra, Pritish, et al. “Efficient Optimization for Rank-Based Loss Functions.” <i>2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition</i>, IEEE, 2018, pp. 3693–701, doi:<a href=\"https://doi.org/10.1109/cvpr.2018.00389\">10.1109/cvpr.2018.00389</a>.","ieee":"P. Mohapatra, M. Rolinek, C. V. Jawahar, V. Kolmogorov, and M. P. Kumar, “Efficient optimization for rank-based loss functions,” in <i>2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition</i>, Salt Lake City, UT, USA, 2018, pp. 3693–3701."},"oa":1,"quality_controlled":"1","year":"2018","date_created":"2018-12-11T11:45:33Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Efficient optimization for rank-based loss functions","ec_funded":1,"main_file_link":[{"url":"https://arxiv.org/abs/1604.08269","open_access":"1"}],"status":"public","abstract":[{"text":"The accuracy of information retrieval systems is often measured using complex loss functions such as the average precision (AP) or the normalized discounted cumulative gain (NDCG). Given a set of positive and negative samples, the parameters of a retrieval system can be estimated by minimizing these loss functions. However, the non-differentiability and non-decomposability of these loss functions does not allow for simple gradient based optimization algorithms. This issue is generally circumvented by either optimizing a structured hinge-loss upper bound to the loss function or by using asymptotic methods like the direct-loss minimization framework. Yet, the high computational complexity of loss-augmented inference, which is necessary for both the frameworks, prohibits its use in large training data sets. To alleviate this deficiency, we present a novel quicksort flavored algorithm for a large class of non-decomposable loss functions. We provide a complete characterization of the loss functions that are amenable to our algorithm, and show that it includes both AP and NDCG based loss functions. Furthermore, we prove that no comparison based algorithm can improve upon the computational complexity of our approach asymptotically. We demonstrate the effectiveness of our approach in the context of optimizing the structured hinge loss upper bound of AP and NDCG loss for learning models for a variety of vision tasks. We show that our approach provides significantly better results than simpler decomposable loss functions, while requiring a comparable training time.","lang":"eng"}],"_id":"273","publication_status":"published","arxiv":1,"day":"28","page":"3693-3701","type":"conference","article_processing_charge":"No","publisher":"IEEE","publication":"2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition","publication_identifier":{"isbn":["9781538664209"]},"doi":"10.1109/cvpr.2018.00389","isi":1,"department":[{"_id":"VlKo"}],"date_updated":"2024-11-04T13:52:32Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160"}],"author":[{"first_name":"Pritish","last_name":"Mohapatra","full_name":"Mohapatra, Pritish"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek","full_name":"Rolinek, Michal"},{"last_name":"Jawahar","full_name":"Jawahar, C V","first_name":"C V"},{"first_name":"Vladimir","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"M Pawan","last_name":"Kumar","full_name":"Kumar, M Pawan"}],"date_published":"2018-06-28T00:00:00Z","oa_version":"Preprint","scopus_import":"1","month":"06","external_id":{"arxiv":["1604.08269"],"isi":["000457843603087"]},"conference":{"end_date":"2018-06-22","start_date":"2018-06-18","location":"Salt Lake City, UT, USA","name":"CVPR: Conference on Computer Vision and Pattern Recognition"},"language":[{"iso":"eng"}]},{"citation":{"ieee":"V. Kolmogorov and M. Rolinek, “Superconcentrators of density 25.3,” <i>Ars Combinatoria</i>, vol. 141, no. 10. Charles Babbage Research Centre, pp. 269–304, 2018.","short":"V. Kolmogorov, M. Rolinek, Ars Combinatoria 141 (2018) 269–304.","mla":"Kolmogorov, Vladimir, and Michal Rolinek. “Superconcentrators of Density 25.3.” <i>Ars Combinatoria</i>, vol. 141, no. 10, Charles Babbage Research Centre, 2018, pp. 269–304.","ista":"Kolmogorov V, Rolinek M. 2018. Superconcentrators of density 25.3. Ars Combinatoria. 141(10), 269–304.","ama":"Kolmogorov V, Rolinek M. Superconcentrators of density 25.3. <i>Ars Combinatoria</i>. 2018;141(10):269-304.","chicago":"Kolmogorov, Vladimir, and Michal Rolinek. “Superconcentrators of Density 25.3.” <i>Ars Combinatoria</i>. Charles Babbage Research Centre, 2018.","apa":"Kolmogorov, V., &#38; Rolinek, M. (2018). Superconcentrators of density 25.3. <i>Ars Combinatoria</i>. Charles Babbage Research Centre."},"oa":1,"quality_controlled":"1","date_created":"2018-12-11T11:44:11Z","year":"2018","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Superconcentrators of density 25.3","publist_id":"8037","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1405.7828"}],"abstract":[{"lang":"eng","text":"An N-superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. We prove the existence of such superconcentrators with asymptotic density 25.3 (where the density is the number of edges divided by N). The previously best known densities were 28 [12] and 27.4136 [17]."}],"_id":"18","intvolume":"       141","status":"public","publication_status":"published","arxiv":1,"volume":141,"day":"01","page":"269 - 304","type":"journal_article","article_processing_charge":"No","issue":"10","publication":"Ars Combinatoria","publisher":"Charles Babbage Research Centre","publication_identifier":{"issn":["0381-7032"]},"isi":1,"department":[{"_id":"VlKo"}],"date_updated":"2023-09-19T14:46:18Z","author":[{"first_name":"Vladimir","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","full_name":"Rolinek, Michal","last_name":"Rolinek"}],"date_published":"2018-10-01T00:00:00Z","oa_version":"Preprint","scopus_import":"1","month":"10","external_id":{"arxiv":["1405.7828"],"isi":["000446809500022"]},"language":[{"iso":"eng"}]},{"isi":1,"department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","doi":"10.1145/3196494.3196534","month":"06","oa_version":"Submitted Version","scopus_import":"1","language":[{"iso":"eng"}],"conference":{"name":"ASIACCS: Asia Conference on Computer and Communications Security ","location":"Incheon, Republic of Korea","start_date":"2018-06-04","end_date":"2018-06-08"},"external_id":{"isi":["000516620100005"]},"date_updated":"2024-11-04T13:52:29Z","project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"},{"name":"Teaching Old Crypto New Tricks","call_identifier":"H2020","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","grant_number":"682815"}],"date_published":"2018-06-01T00:00:00Z","author":[{"full_name":"Alwen, Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","last_name":"Alwen","first_name":"Joel F"},{"full_name":"Gazi, Peter","last_name":"Gazi","first_name":"Peter"},{"first_name":"Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","last_name":"Kamath Hosdurg","full_name":"Kamath Hosdurg, Chethan"},{"id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","last_name":"Klein","full_name":"Klein, Karen","first_name":"Karen"},{"last_name":"Osang","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","orcid":"0000-0002-8882-5116"},{"last_name":"Pietrzak","full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof Z","orcid":"0000-0002-9139-1654"},{"first_name":"Lenoid","full_name":"Reyzin, Lenoid","last_name":"Reyzin"},{"full_name":"Rolinek, Michal","last_name":"Rolinek","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal"},{"first_name":"Michal","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","last_name":"Rybar","full_name":"Rybar, Michal"}],"title":"On the memory hardness of data independent password hashing functions","ec_funded":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"7723","oa":1,"citation":{"ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>. ACM; 2018:51-65. doi:<a href=\"https://doi.org/10.1145/3196494.3196534\">10.1145/3196494.3196534</a>","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i> (pp. 51–65). Incheon, Republic of Korea: ACM. <a href=\"https://doi.org/10.1145/3196494.3196534\">https://doi.org/10.1145/3196494.3196534</a>","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, 51–65. ACM, 2018. <a href=\"https://doi.org/10.1145/3196494.3196534\">https://doi.org/10.1145/3196494.3196534</a>.","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","ieee":"J. F. Alwen <i>et al.</i>, “On the memory hardness of data independent password hashing functions,” in <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, Incheon, Republic of Korea, 2018, pp. 51–65.","mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, ACM, 2018, pp. 51–65, doi:<a href=\"https://doi.org/10.1145/3196494.3196534\">10.1145/3196494.3196534</a>."},"date_created":"2018-12-11T11:45:07Z","year":"2018","quality_controlled":"1","type":"conference","day":"01","page":"51 - 65","publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","publisher":"ACM","article_processing_charge":"No","_id":"193","abstract":[{"lang":"eng","text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF."}],"status":"public","main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/783"}],"publication_status":"published"},{"status":"public","_id":"10864","abstract":[{"lang":"eng","text":"We prove that every congruence distributive variety has directed Jónsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original Jónsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in congruence distributive and congruence modular varieties, respectively. For finite algebras, these absorption theorems have already seen significant applications, but until now, it was not clear if the theorems hold for general algebras as well. Our method also yields a novel proof of a result by P. Lipparini about the existence of a chain of terms (which we call Pixley terms) in varieties that are at the same time congruence distributive and k-permutable for some k."}],"intvolume":"        16","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1502.01072"}],"arxiv":1,"publication_status":"published","series_title":"OCTR","type":"book_chapter","page":"203-220","day":"21","volume":16,"publisher":"Springer Nature","publication":"Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science","article_processing_charge":"No","oa":1,"citation":{"mla":"Kazda, Alexandr, et al. “Absorption and Directed Jónsson Terms.” <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science</i>, edited by J Czelakowski, vol. 16, Springer Nature, 2018, pp. 203–20, doi:<a href=\"https://doi.org/10.1007/978-3-319-74772-9_7\">10.1007/978-3-319-74772-9_7</a>.","short":"A. Kazda, M. Kozik, R. McKenzie, M. Moore, in:, J. Czelakowski (Ed.), Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science, Springer Nature, Cham, 2018, pp. 203–220.","ieee":"A. Kazda, M. Kozik, R. McKenzie, and M. Moore, “Absorption and directed Jónsson terms,” in <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science</i>, vol. 16, J. Czelakowski, Ed. Cham: Springer Nature, 2018, pp. 203–220.","apa":"Kazda, A., Kozik, M., McKenzie, R., &#38; Moore, M. (2018). Absorption and directed Jónsson terms. In J. Czelakowski (Ed.), <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science</i> (Vol. 16, pp. 203–220). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-74772-9_7\">https://doi.org/10.1007/978-3-319-74772-9_7</a>","chicago":"Kazda, Alexandr, Marcin Kozik, Ralph McKenzie, and Matthew Moore. “Absorption and Directed Jónsson Terms.” In <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science</i>, edited by J Czelakowski, 16:203–20. OCTR. Cham: Springer Nature, 2018. <a href=\"https://doi.org/10.1007/978-3-319-74772-9_7\">https://doi.org/10.1007/978-3-319-74772-9_7</a>.","ama":"Kazda A, Kozik M, McKenzie R, Moore M. Absorption and directed Jónsson terms. In: Czelakowski J, ed. <i>Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science</i>. Vol 16. OCTR. Cham: Springer Nature; 2018:203-220. doi:<a href=\"https://doi.org/10.1007/978-3-319-74772-9_7\">10.1007/978-3-319-74772-9_7</a>","ista":"Kazda A, Kozik M, McKenzie R, Moore M. 2018.Absorption and directed Jónsson terms. In: Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. vol. 16, 203–220."},"year":"2018","date_created":"2022-03-18T10:30:32Z","quality_controlled":"1","corr_author":"1","title":"Absorption and directed Jónsson terms","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2024-10-09T21:01:50Z","date_published":"2018-03-21T00:00:00Z","author":[{"id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87","full_name":"Kazda, Alexandr","last_name":"Kazda","first_name":"Alexandr"},{"full_name":"Kozik, Marcin","last_name":"Kozik","first_name":"Marcin"},{"last_name":"McKenzie","full_name":"McKenzie, Ralph","first_name":"Ralph"},{"last_name":"Moore","full_name":"Moore, Matthew","first_name":"Matthew"}],"place":"Cham","month":"03","scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"external_id":{"arxiv":["1502.01072"]},"publication_identifier":{"isbn":["9783319747712"],"eissn":["2211-2766"],"eisbn":["9783319747729"],"issn":["2211-2758"]},"editor":[{"last_name":"Czelakowski","full_name":"Czelakowski, J","first_name":"J"}],"acknowledgement":"The second author was supported by National Science Center grant DEC-2011-/01/B/ST6/01006.","doi":"10.1007/978-3-319-74772-9_7","department":[{"_id":"VlKo"}]},{"ddc":["001"],"date_published":"2018-01-04T00:00:00Z","file":[{"checksum":"53c17082848e12f3c2e1b4185b578208","file_size":1737958,"file_id":"5600","access_level":"open_access","content_type":"application/zip","relation":"main_file","date_created":"2018-12-12T13:02:34Z","file_name":"IST-2018-82-v1+1_GraphFlowMatchingProblems.zip","creator":"system","date_updated":"2020-07-14T12:47:05Z"}],"author":[{"first_name":"Hassan","last_name":"Alhaija","full_name":"Alhaija, Hassan"},{"first_name":"Anita","last_name":"Sellent","full_name":"Sellent, Anita"},{"full_name":"Kondermann, Daniel","last_name":"Kondermann","first_name":"Daniel"},{"first_name":"Carsten","last_name":"Rother","full_name":"Rother, Carsten"}],"date_updated":"2024-02-21T13:41:17Z","status":"public","_id":"5573","abstract":[{"lang":"eng","text":"Graph matching problems for large displacement optical flow of RGB-D images."}],"publisher":"Institute of Science and Technology Austria","article_processing_charge":"No","type":"research_data","contributor":[{"contributor_type":"researcher","first_name":"Paul","id":"446560C6-F248-11E8-B48F-1D18A9856A87","last_name":"Swoboda"}],"month":"01","day":"04","has_accepted_license":"1","keyword":["graph matching","quadratic assignment problem<"],"oa_version":"Published Version","year":"2018","doi":"10.15479/AT:ISTA:82","date_created":"2018-12-12T12:31:36Z","oa":1,"license":"https://creativecommons.org/publicdomain/zero/1.0/","citation":{"short":"H. Alhaija, A. Sellent, D. Kondermann, C. Rother, (2018).","mla":"Alhaija, Hassan, et al. <i>Graph Matching Problems for GraphFlow – 6D Large Displacement Scene Flow</i>. Institute of Science and Technology Austria, 2018, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:82\">10.15479/AT:ISTA:82</a>.","ieee":"H. Alhaija, A. Sellent, D. Kondermann, and C. Rother, “Graph matching problems for GraphFlow – 6D Large Displacement Scene Flow.” Institute of Science and Technology Austria, 2018.","chicago":"Alhaija, Hassan, Anita Sellent, Daniel Kondermann, and Carsten Rother. “Graph Matching Problems for GraphFlow – 6D Large Displacement Scene Flow.” Institute of Science and Technology Austria, 2018. <a href=\"https://doi.org/10.15479/AT:ISTA:82\">https://doi.org/10.15479/AT:ISTA:82</a>.","apa":"Alhaija, H., Sellent, A., Kondermann, D., &#38; Rother, C. (2018). Graph matching problems for GraphFlow – 6D Large Displacement Scene Flow. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:82\">https://doi.org/10.15479/AT:ISTA:82</a>","ista":"Alhaija H, Sellent A, Kondermann D, Rother C. 2018. Graph matching problems for GraphFlow – 6D Large Displacement Scene Flow, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:82\">10.15479/AT:ISTA:82</a>.","ama":"Alhaija H, Sellent A, Kondermann D, Rother C. Graph matching problems for GraphFlow – 6D Large Displacement Scene Flow. 2018. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:82\">10.15479/AT:ISTA:82</a>"},"datarep_id":"82","title":"Graph matching problems for GraphFlow – 6D Large Displacement Scene Flow","file_date_updated":"2020-07-14T12:47:05Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"link":[{"url":"https://doi.org/10.1007/978-3-319-24947-6_23","relation":"research_paper"}]},"tmp":{"short":"CC0 (1.0)","name":"Creative Commons Public Domain Dedication (CC0 1.0)","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","image":"/images/cc_0.png"},"department":[{"_id":"VlKo"}]},{"related_material":{"record":[{"status":"public","id":"1193","relation":"earlier_version"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"title":"Commutativity in the algorithmic Lovász local lemma","citation":{"short":"V. Kolmogorov, SIAM Journal on Computing 47 (2018) 2029–2056.","mla":"Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovász Local Lemma.” <i>SIAM Journal on Computing</i>, vol. 47, no. 6, Society for Industrial and Applied Mathematics, 2018, pp. 2029–56, doi:<a href=\"https://doi.org/10.1137/16m1093306\">10.1137/16m1093306</a>.","ieee":"V. Kolmogorov, “Commutativity in the algorithmic Lovász local lemma,” <i>SIAM Journal on Computing</i>, vol. 47, no. 6. Society for Industrial and Applied Mathematics, pp. 2029–2056, 2018.","apa":"Kolmogorov, V. (2018). Commutativity in the algorithmic Lovász local lemma. <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/16m1093306\">https://doi.org/10.1137/16m1093306</a>","chicago":"Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovász Local Lemma.” <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics, 2018. <a href=\"https://doi.org/10.1137/16m1093306\">https://doi.org/10.1137/16m1093306</a>.","ama":"Kolmogorov V. Commutativity in the algorithmic Lovász local lemma. <i>SIAM Journal on Computing</i>. 2018;47(6):2029-2056. doi:<a href=\"https://doi.org/10.1137/16m1093306\">10.1137/16m1093306</a>","ista":"Kolmogorov V. 2018. Commutativity in the algorithmic Lovász local lemma. SIAM Journal on Computing. 47(6), 2029–2056."},"oa":1,"quality_controlled":"1","date_created":"2019-02-13T12:59:33Z","year":"2018","volume":47,"page":"2029-2056","day":"08","type":"journal_article","article_processing_charge":"No","publication":"SIAM Journal on Computing","issue":"6","publisher":"Society for Industrial and Applied Mathematics","main_file_link":[{"url":"https://arxiv.org/abs/1506.08547","open_access":"1"}],"intvolume":"        47","_id":"5975","abstract":[{"text":"We consider the recent formulation of the algorithmic Lov ́asz Local Lemma  [N. Har-vey and J. Vondr ́ak, inProceedings of FOCS, 2015, pp. 1327–1345; D. Achlioptas and F. Iliopoulos,inProceedings of SODA, 2016, pp. 2024–2038; D. Achlioptas, F. Iliopoulos, and V. Kolmogorov,ALocal Lemma for Focused Stochastic Algorithms, arXiv preprint, 2018] for finding objects that avoid“bad  features,”  or  “flaws.”   It  extends  the  Moser–Tardos  resampling  algorithm  [R.  A.  Moser  andG. Tardos,J. ACM, 57 (2010), 11] to more general discrete spaces.  At each step the method picks aflaw present in the current state and goes to a new state according to some prespecified probabilitydistribution (which depends on the current state and the selected flaw).  However, the recent formu-lation is less flexible than the Moser–Tardos method since it requires a specific flaw selection rule,whereas the algorithm of Moser and Tardos allows an arbitrary rule (and thus can potentially beimplemented more efficiently).  We formulate a new “commutativity” condition and prove that it issufficient for an arbitrary rule to work.  It also enables an efficient parallelization under an additionalassumption.  We then show that existing resampling oracles for perfect matchings and permutationsdo satisfy this condition.","lang":"eng"}],"status":"public","publication_status":"published","arxiv":1,"isi":1,"department":[{"_id":"VlKo"}],"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"doi":"10.1137/16m1093306","scopus_import":"1","oa_version":"Preprint","month":"11","external_id":{"arxiv":["1506.08547"],"isi":["000453785100001"]},"language":[{"iso":"eng"}],"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"date_updated":"2025-09-22T09:44:20Z","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir"}],"date_published":"2018-11-08T00:00:00Z"},{"date_published":"2018-02-01T00:00:00Z","arxiv":1,"publication_status":"published","author":[{"last_name":"Haller","full_name":"Haller, Stefan","first_name":"Stefan"},{"full_name":"Swoboda, Paul","last_name":"Swoboda","id":"446560C6-F248-11E8-B48F-1D18A9856A87","first_name":"Paul"},{"full_name":"Savchynskyy, Bogdan","last_name":"Savchynskyy","first_name":"Bogdan"}],"abstract":[{"text":"We consider the MAP-inference problem for graphical models,which is a valued constraint satisfaction problem defined onreal numbers with a natural summation operation. We proposea family of relaxations (different from the famous Sherali-Adams hierarchy), which naturally define lower bounds for itsoptimum. This family always contains a tight relaxation andwe give an algorithm able to find it and therefore, solve theinitial non-relaxed NP-hard problem.The relaxations we consider decompose the original probleminto two non-overlapping parts: an easy LP-tight part and adifficult one. For the latter part a combinatorial solver must beused. As we show in our experiments, in a number of applica-tions the second, difficult part constitutes only a small fractionof the whole problem. This property allows to significantlyreduce the computational time of the combinatorial solver andtherefore solve problems which were out of reach before.","lang":"eng"}],"_id":"5978","status":"public","date_updated":"2023-09-19T14:26:52Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2004.06370"}],"language":[{"iso":"eng"}],"publication":"Proceedings of the 32st AAAI Conference on Artificial Intelligence","conference":{"location":"New Orleans, LU, United States","name":"AAAI: Conference on Artificial Intelligence","end_date":"2018-02-07","start_date":"2018-02-02"},"publisher":"AAAI Press","external_id":{"isi":["000485488906082"],"arxiv":["2004.06370"]},"article_processing_charge":"No","month":"02","type":"conference","oa_version":"Preprint","scopus_import":"1","day":"01","page":"6581-6588","date_created":"2019-02-13T13:32:48Z","year":"2018","quality_controlled":"1","oa":1,"citation":{"chicago":"Haller, Stefan, Paul Swoboda, and Bogdan Savchynskyy. “Exact MAP-Inference by Confining Combinatorial Search with LP Relaxation.” In <i>Proceedings of the 32st AAAI Conference on Artificial Intelligence</i>, 6581–88. AAAI Press, 2018.","apa":"Haller, S., Swoboda, P., &#38; Savchynskyy, B. (2018). Exact MAP-inference by confining combinatorial search with LP relaxation. In <i>Proceedings of the 32st AAAI Conference on Artificial Intelligence</i> (pp. 6581–6588). New Orleans, LU, United States: AAAI Press.","ista":"Haller S, Swoboda P, Savchynskyy B. 2018. Exact MAP-inference by confining combinatorial search with LP relaxation. Proceedings of the 32st AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence, 6581–6588.","ama":"Haller S, Swoboda P, Savchynskyy B. Exact MAP-inference by confining combinatorial search with LP relaxation. In: <i>Proceedings of the 32st AAAI Conference on Artificial Intelligence</i>. AAAI Press; 2018:6581-6588.","mla":"Haller, Stefan, et al. “Exact MAP-Inference by Confining Combinatorial Search with LP Relaxation.” <i>Proceedings of the 32st AAAI Conference on Artificial Intelligence</i>, AAAI Press, 2018, pp. 6581–88.","short":"S. Haller, P. Swoboda, B. Savchynskyy, in:, Proceedings of the 32st AAAI Conference on Artificial Intelligence, AAAI Press, 2018, pp. 6581–6588.","ieee":"S. Haller, P. Swoboda, and B. Savchynskyy, “Exact MAP-inference by confining combinatorial search with LP relaxation,” in <i>Proceedings of the 32st AAAI Conference on Artificial Intelligence</i>, New Orleans, LU, United States, 2018, pp. 6581–6588."},"title":"Exact MAP-inference by confining combinatorial search with LP relaxation","isi":1,"department":[{"_id":"VlKo"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"article_type":"original","quality_controlled":"1","year":"2018","date_created":"2019-02-17T22:59:25Z","citation":{"short":"A. Kazda, V. Kolmogorov, M. Rolinek, ACM Transactions on Algorithms 15 (2018).","ieee":"A. Kazda, V. Kolmogorov, and M. Rolinek, “Even delta-matroids and the complexity of planar boolean CSPs,” <i>ACM Transactions on Algorithms</i>, vol. 15, no. 2. ACM, 2018.","mla":"Kazda, Alexandr, et al. “Even Delta-Matroids and the Complexity of Planar Boolean CSPs.” <i>ACM Transactions on Algorithms</i>, vol. 15, no. 2, 22, ACM, 2018, doi:<a href=\"https://doi.org/10.1145/3230649\">10.1145/3230649</a>.","apa":"Kazda, A., Kolmogorov, V., &#38; Rolinek, M. (2018). Even delta-matroids and the complexity of planar boolean CSPs. <i>ACM Transactions on Algorithms</i>. ACM. <a href=\"https://doi.org/10.1145/3230649\">https://doi.org/10.1145/3230649</a>","chicago":"Kazda, Alexandr, Vladimir Kolmogorov, and Michal Rolinek. “Even Delta-Matroids and the Complexity of Planar Boolean CSPs.” <i>ACM Transactions on Algorithms</i>. ACM, 2018. <a href=\"https://doi.org/10.1145/3230649\">https://doi.org/10.1145/3230649</a>.","ama":"Kazda A, Kolmogorov V, Rolinek M. Even delta-matroids and the complexity of planar boolean CSPs. <i>ACM Transactions on Algorithms</i>. 2018;15(2). doi:<a href=\"https://doi.org/10.1145/3230649\">10.1145/3230649</a>","ista":"Kazda A, Kolmogorov V, Rolinek M. 2018. Even delta-matroids and the complexity of planar boolean CSPs. ACM Transactions on Algorithms. 15(2), 22."},"oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"1192"}]},"title":"Even delta-matroids and the complexity of planar boolean CSPs","ec_funded":1,"publication_status":"published","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.03124"}],"status":"public","abstract":[{"text":"The main result of this article is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Δ-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Using a reduction to even Δ-matroids, we then extend the tractability result to larger classes of Δ-matroids that we call efficiently coverable. It properly includes classes that were known to be tractable before, namely, co-independent, compact, local, linear, and binary, with the following caveat:We represent Δ-matroids by lists of tuples, while the last two use a representation by matrices. Since an n ×n matrix can represent exponentially many tuples, our tractability result is not strictly stronger than the known algorithm for linear and binary Δ-matroids.","lang":"eng"}],"_id":"6032","intvolume":"        15","article_processing_charge":"No","publisher":"ACM","issue":"2","publication":"ACM Transactions on Algorithms","day":"01","volume":15,"type":"journal_article","doi":"10.1145/3230649","article_number":"22","isi":1,"department":[{"_id":"VlKo"}],"author":[{"first_name":"Alexandr","last_name":"Kazda","full_name":"Kazda, Alexandr","id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"},{"full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek","first_name":"Michal"}],"date_published":"2018-12-01T00:00:00Z","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160"}],"date_updated":"2025-06-04T08:46:58Z","external_id":{"arxiv":["1602.03124"],"isi":["000468036500007"]},"language":[{"iso":"eng"}],"scopus_import":"1","oa_version":"Preprint","month":"12"}]