[{"department":[{"_id":"GradSch"},{"_id":"VlKo"}],"abstract":[{"text":"Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and results about totally unimodular matrices, vector matroids, their standard representations, regular matroids, and 1-, 2-, and 3-sums of matrices and binary matroids given by their standard representations. Using this framework, we formally state Seymour's decomposition theorem and implement a formally verified proof of the composition direction in the setting where the matroids have finite rank and may have infinite ground sets.","lang":"eng"}],"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2509.20539","open_access":"1"}],"citation":{"ista":"Dvorak M, Figueroa-Reid T, Hamadani R, Hwang B-H, Karunus E, Kolmogorov V, Meiburg A, Nelson A, Nelson P, Sandey M, Sergeev I. Composition direction of Seymour’s theorem for regular matroids — Formally verified. arXiv, 2509.20539.","short":"M. Dvorak, T. Figueroa-Reid, R. Hamadani, B.-H. Hwang, E. Karunus, V. Kolmogorov, A. Meiburg, A. Nelson, P. Nelson, M. Sandey, I. Sergeev, ArXiv (n.d.).","chicago":"Dvorak, Martin, Tristan Figueroa-Reid, Rida Hamadani, Byung-Hak Hwang, Evgenia Karunus, Vladimir Kolmogorov, Alexander Meiburg, et al. “Composition Direction of Seymour’s Theorem for Regular Matroids — Formally Verified.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2509.20539.","ama":"Dvorak M, Figueroa-Reid T, Hamadani R, et al. Composition direction of Seymour’s theorem for regular matroids — Formally verified. arXiv. doi:10.48550/arXiv.2509.20539","ieee":"M. Dvorak et al., “Composition direction of Seymour’s theorem for regular matroids — Formally verified,” arXiv. .","apa":"Dvorak, M., Figueroa-Reid, T., Hamadani, R., Hwang, B.-H., Karunus, E., Kolmogorov, V., … Sergeev, I. (n.d.). Composition direction of Seymour’s theorem for regular matroids — Formally verified. arXiv. https://doi.org/10.48550/arXiv.2509.20539","mla":"Dvorak, Martin, et al. “Composition Direction of Seymour’s Theorem for Regular Matroids — Formally Verified.” ArXiv, 2509.20539, doi:10.48550/arXiv.2509.20539."},"doi":"10.48550/arXiv.2509.20539","author":[{"first_name":"Martin","full_name":"Dvorak, Martin","last_name":"Dvorak","orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425"},{"last_name":"Figueroa-Reid","first_name":"Tristan","full_name":"Figueroa-Reid, Tristan"},{"last_name":"Hamadani","full_name":"Hamadani, Rida","first_name":"Rida"},{"full_name":"Hwang, Byung-Hak","first_name":"Byung-Hak","last_name":"Hwang"},{"last_name":"Karunus","full_name":"Karunus, Evgenia","first_name":"Evgenia"},{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Meiburg","full_name":"Meiburg, Alexander","first_name":"Alexander"},{"full_name":"Nelson, Alexander","first_name":"Alexander","last_name":"Nelson"},{"first_name":"Peter","full_name":"Nelson, Peter","last_name":"Nelson"},{"last_name":"Sandey","first_name":"Mark","full_name":"Sandey, Mark"},{"id":"ca3c9187-9a72-11ee-a009-8af825d896b0","orcid":"0009-0004-9145-8785","last_name":"Sergeev","full_name":"Sergeev, Ivan","first_name":"Ivan"}],"external_id":{"arxiv":["2509.20539"]},"OA_place":"repository","status":"public","date_created":"2026-03-04T11:56:29Z","das_tickbox":"1","OA_type":"green","date_updated":"2026-07-29T12:56:51Z","publication_status":"draft","month":"09","_id":"21398","oa_version":"Preprint","year":"2025","arxiv":1,"language":[{"iso":"eng"}],"acknowledgement":"We would like to dedicate the paper to the memory of Klaus Truemper, whose monograph Matroid Decomposition [12]\r\nlaid the foundation for our entire work.","type":"preprint","publication":"arXiv","article_number":"2509.20539","title":"Composition direction of Seymour's theorem for regular matroids — Formally verified","day":"23","fulldoi":"https://doi.org/10.48550/arXiv.2509.20539","date_published":"2025-09-23T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"21393","status":"public"}]}},{"acknowledgement":"This extended abstract is based on the paper [7], accepted for publication at SIAM\r\nJ. Opt. on April 22, 2025, to which we refer for technical details and complete proofs. This work has been\r\nsupported by the Doctoral Programme Vienna Graduate School on Computational Optimization (VGSCO)\r\nwhich was funded by FWF (Austrian Science Fund), project W 1260-N35, and partially supported by the\r\nANR JCJC project ANR-21-CE48-0006-01 “HYPERSPACE”.\r\n","language":[{"iso":"eng"}],"type":"journal_article","volume":59,"article_type":"original","year":"2025","oa_version":"Published Version","_id":"22774","oa":1,"date_published":"2025-12-01T00:00:00Z","fulldoi":"https://doi.org/10.1145/3832046.3832063","corr_author":"1","page":"147-152","publication_identifier":{"eissn":["1932-2240"],"issn":["1932-2232"]},"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"ACM Communications in Computer Algebra","day":"01","title":"Certifying solutions of degenerate semidefinite programs","citation":{"short":"V. Kolmogorov, S. Naldi, J. Zapata, ACM Communications in Computer Algebra 59 (2025) 147–152.","ista":"Kolmogorov V, Naldi S, Zapata J. 2025. Certifying solutions of degenerate semidefinite programs. ACM Communications in Computer Algebra. 59(4), 147–152.","ama":"Kolmogorov V, Naldi S, Zapata J. Certifying solutions of degenerate semidefinite programs. ACM Communications in Computer Algebra. 2025;59(4):147-152. doi:10.1145/3832046.3832063","apa":"Kolmogorov, V., Naldi, S., & Zapata, J. (2025). Certifying solutions of degenerate semidefinite programs. ACM Communications in Computer Algebra. ACM. https://doi.org/10.1145/3832046.3832063","ieee":"V. Kolmogorov, S. Naldi, and J. Zapata, “Certifying solutions of degenerate semidefinite programs,” ACM Communications in Computer Algebra, vol. 59, no. 4. ACM, pp. 147–152, 2025.","chicago":"Kolmogorov, Vladimir, Simone Naldi, and Jeferson Zapata. “Certifying Solutions of Degenerate Semidefinite Programs.” ACM Communications in Computer Algebra. ACM, 2025. https://doi.org/10.1145/3832046.3832063.","mla":"Kolmogorov, Vladimir, et al. “Certifying Solutions of Degenerate Semidefinite Programs.” ACM Communications in Computer Algebra, vol. 59, no. 4, ACM, 2025, pp. 147–52, doi:10.1145/3832046.3832063."},"author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov"},{"last_name":"Naldi","full_name":"Naldi, Simone","first_name":"Simone"},{"full_name":"Zapata, Jeferson","first_name":"Jeferson","last_name":"Zapata","id":"00223538-AF8F-11E9-A4C7-F729E6697425"}],"doi":"10.1145/3832046.3832063","intvolume":" 59","publisher":"ACM","article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.1145/3832046.3832063","open_access":"1"}],"abstract":[{"text":"We consider the problem of certifying the feasibility of a (possibly degenerate) semidefinite programming problem represented by rational input data together with a numerical solution that is guaranteed to be sufficiently close to an exact solution of maximal rank. Our method constructs a polynomial system whose set of real solutions has an isolated point that satisfies the input program. An experimental comparison between the corresponding symbolic-numerical algorithm and the purely symbolic algorithm from [3, 5] shows that the hybrid algorithm is able to certify instances where the exact method fails.","lang":"eng"}],"department":[{"_id":"VlKo"}],"publication_status":"published","date_updated":"2026-09-09T08:17:05Z","issue":"4","project":[{"_id":"9B9290DE-BA93-11EA-9121-9846C619BF3A","grant_number":"W1260-N35","name":"Vienna Graduate School on Computational Optimization"}],"month":"12","external_id":{"unknown":["2405.13625"]},"OA_type":"free access","date_created":"2026-08-30T22:01:44Z","status":"public","OA_place":"publisher"},{"doi":"10.1007/s10107-024-02064-5","intvolume":" 209","author":[{"last_name":"Dvorak","orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","first_name":"Martin","full_name":"Dvorak, Martin"},{"first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"apa":"Dvorak, M., & Kolmogorov, V. (2025). Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. Springer Nature. https://doi.org/10.1007/s10107-024-02064-5","ama":"Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 2025;209:279-322. doi:10.1007/s10107-024-02064-5","ieee":"M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and discrete convexity,” Mathematical Programming, vol. 209. Springer Nature, pp. 279–322, 2025.","chicago":"Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” Mathematical Programming. Springer Nature, 2025. https://doi.org/10.1007/s10107-024-02064-5.","mla":"Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” Mathematical Programming, vol. 209, Springer Nature, 2025, pp. 279–322, doi:10.1007/s10107-024-02064-5.","ista":"Dvorak M, Kolmogorov V. 2025. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 209, 279–322.","short":"M. Dvorak, V. Kolmogorov, Mathematical Programming 209 (2025) 279–322."},"ddc":["004"],"file_date_updated":"2025-04-16T09:36:08Z","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"abstract":[{"lang":"eng","text":"Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n"}],"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","has_accepted_license":"1","month":"01","date_updated":"2026-10-02T11:45:16Z","publication_status":"published","status":"public","OA_place":"publisher","OA_type":"hybrid","date_created":"2021-09-27T10:48:23Z","das_tickbox":"0","external_id":{"isi":["001176563300001"],"arxiv":["2109.10203"]},"supplementarymaterial":"no","quality_controlled":"1","volume":209,"type":"journal_article","file":[{"success":1,"date_created":"2025-04-16T09:36:08Z","file_id":"19578","date_updated":"2025-04-16T09:36:08Z","file_name":"2025_MathProgramming_Dvorak.pdf","relation":"main_file","creator":"dernst","file_size":839510,"content_type":"application/pdf","checksum":"25d9bd490719b45eca84f4d93a06c69f","access_level":"open_access"}],"language":[{"iso":"eng"}],"acknowledgement":"We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Open access funding provided by Institute of Science and Technology (IST Austria).","year":"2025","arxiv":1,"_id":"10045","oa_version":"Published Version","keyword":["minimum 0-extension problem","metric labeling problem","discrete metric spaces","metric extensions","computational complexity","valued constraint satisfaction problems","discrete convex analysis","L-convex functions"],"article_type":"original","publication_identifier":{"eissn":["1436-4646"],"issn":["0025-5610"]},"scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","page":"279-322","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"date_published":"2025-01-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s10107-024-02064-5","isi":1,"oa":1,"title":"Generalized minimum 0-extension problem and discrete convexity","day":"01","researchdata_availability":"no","publication":"Mathematical Programming"},{"date_published":"2024-06-17T00:00:00Z","fulldoi":"https://doi.org/10.1145/3626183.3659969","isi":1,"oa":1,"scopus_import":"1","publication_identifier":{"issn":["1548-6109"],"isbn":["9798400704161"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","related_material":{"record":[{"relation":"extended_version","id":"21007","status":"public"}]},"page":"403-414","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication":"Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures","title":"A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut","day":"17","language":[{"iso":"eng"}],"file":[{"date_created":"2024-07-16T06:38:08Z","success":1,"creator":"dernst","file_size":1116166,"content_type":"application/pdf","access_level":"open_access","checksum":"6ca18ac8508719dbd5d5735f4c991af2","file_id":"17245","date_updated":"2024-07-16T06:38:08Z","relation":"main_file","file_name":"2024_SPAA_Kolmogorov.pdf"}],"type":"conference","arxiv":1,"year":"2024","_id":"17236","oa_version":"Published Version","date_updated":"2026-01-21T09:46:25Z","publication_status":"published","month":"06","external_id":{"arxiv":["2307.00115"],"isi":["001253331900044"]},"conference":{"start_date":"2024-06-17","name":"SPAA: Symposium on Parallelism in Algorithms and Architectures","end_date":"2024-06-21","location":"Nantes, France"},"quality_controlled":"1","OA_place":"publisher","status":"public","OA_type":"hybrid","date_created":"2024-07-14T22:01:11Z","ddc":["510"],"citation":{"short":"V. Kolmogorov, in:, Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, Association for Computing Machinery, 2024, pp. 403–414.","ista":"Kolmogorov V. 2024. A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut. Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures. SPAA: Symposium on Parallelism in Algorithms and Architectures, 403–414.","mla":"Kolmogorov, Vladimir. “A Simpler and Parallelizable O(√log n)-Approximation Algorithm for Sparsest Cut.” Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, Association for Computing Machinery, 2024, pp. 403–14, doi:10.1145/3626183.3659969.","chicago":"Kolmogorov, Vladimir. “A Simpler and Parallelizable O(√log n)-Approximation Algorithm for Sparsest Cut.” In Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, 403–14. Association for Computing Machinery, 2024. https://doi.org/10.1145/3626183.3659969.","ama":"Kolmogorov V. A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut. In: Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures. Association for Computing Machinery; 2024:403-414. doi:10.1145/3626183.3659969","ieee":"V. Kolmogorov, “A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut,” in Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, Nantes, France, 2024, pp. 403–414.","apa":"Kolmogorov, V. (2024). A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut. In Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures (pp. 403–414). Nantes, France: Association for Computing Machinery. https://doi.org/10.1145/3626183.3659969"},"doi":"10.1145/3626183.3659969","author":[{"last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"}],"publisher":"Association for Computing Machinery","has_accepted_license":"1","file_date_updated":"2024-07-16T06:38:08Z","department":[{"_id":"VlKo"}],"abstract":[{"lang":"eng","text":"Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes O(√(log n)/ε)-approximation using O(nε logO(1) n) maxflows for any ε∈[Θ(1/log n),Θ(1)]. It works by solving the SDP relaxation of [Arora-Rao-Vazirani, STOC 2004] using the Multiplicative Weights Update algorithm (MW) of [Arora-Kale, JACM 2016]. To implement one MW step, Sherman approximately solves a multicommodity flow problem using another application of MW. Nested MW steps are solved via a certain \"chaining\" algorithm that combines results of multiple calls to the maxflow algorithm.\r\nWe present an alternative approach that avoids solving the multicommodity flow problem and instead computes \"violating paths\". This simplifies Sherman's algorithm by removing a need for a nested application of MW, and also allows parallelization: we show how to compute O(√(log n)/ε)-approximation via O(logO(1) n) maxflows using O(nε) processors.\r\nWe also revisit Sherman's chaining algorithm, and present a simpler version together with a new analysis."}],"article_processing_charge":"Yes (via OA deal)"},{"department":[{"_id":"GradSch"},{"_id":"VlKo"}],"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.08119","open_access":"1"}],"abstract":[{"text":"Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take \"infinite values\".","lang":"eng"}],"citation":{"chicago":"Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization and Its Extensions -- Formally Verified.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.08119.","apa":"Dvorak, M., & Kolmogorov, V. (n.d.). Duality theory in linear optimization and its extensions -- formally verified. arXiv. https://doi.org/10.48550/arXiv.2409.08119","ama":"Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions -- formally verified. arXiv. doi:10.48550/arXiv.2409.08119","ieee":"M. Dvorak and V. Kolmogorov, “Duality theory in linear optimization and its extensions -- formally verified,” arXiv. .","mla":"Dvorak, Martin, and Vladimir Kolmogorov. “Duality Theory in Linear Optimization and Its Extensions -- Formally Verified.” ArXiv, 2409.08119, doi:10.48550/arXiv.2409.08119.","short":"M. Dvorak, V. Kolmogorov, ArXiv (n.d.).","ista":"Dvorak M, Kolmogorov V. Duality theory in linear optimization and its extensions -- formally verified. arXiv, 2409.08119."},"doi":"10.48550/arXiv.2409.08119","author":[{"orcid":"0000-0001-5293-214X","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","last_name":"Dvorak","first_name":"Martin","full_name":"Dvorak, Martin"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"}],"external_id":{"arxiv":["2409.08119"]},"status":"public","OA_place":"repository","date_created":"2025-07-23T11:21:52Z","OA_type":"green","date_updated":"2026-07-29T12:56:51Z","publication_status":"draft","month":"09","keyword":["Farkas lemma","linear programming","extended reals","calculus of inductive constructions"],"oa_version":"Preprint","_id":"20071","arxiv":1,"year":"2024","language":[{"iso":"eng"}],"acknowledgement":"We would like to thank David Bartl and Jasmin Blanchette for frequent consultations. We would also like to express gratitude to Andrew Yang for the proof of Finset.univ sum of zero when not and to Henrik B¨oving for a help with generalization from extended rationals to extended linearly ordered fields. We would also like to acknowledge Antoine Chambert-Loir, Apurva Nakade, Ya¨el Dillies, Richard Copley, Edward van de Meent, Markus Himmel, Mario Carneiro, and Kevin Buzzard.","type":"preprint","publication":"arXiv","article_number":"2409.08119","title":"Duality theory in linear optimization and its extensions -- formally verified","day":"12","fulldoi":"https://doi.org/10.48550/arXiv.2409.08119","date_published":"2024-09-12T00:00:00Z","oa":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","related_material":{"record":[{"id":"22607","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"21393"}],"link":[{"description":"full version of all definitions, statement, and proofs","relation":"software","url":"https://github.com/madvorak/duality/tree/v3.2"}]},"corr_author":"1"},{"intvolume":" 261","doi":"10.4230/LIPIcs.ICALP.2023.72","author":[{"last_name":"Harris","first_name":"David G.","full_name":"Harris, David G."},{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"mla":"Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” 50th International Colloquium on Automata, Languages, and Programming, vol. 261, 72, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ICALP.2023.72.","ieee":"D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,” in 50th International Colloquium on Automata, Languages, and Programming, Paderborn, Germany, 2023, vol. 261.","apa":"Harris, D. G., & Kolmogorov, V. (2023). Parameter estimation for Gibbs distributions. In 50th International Colloquium on Automata, Languages, and Programming (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.72","ama":"Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. In: 50th International Colloquium on Automata, Languages, and Programming. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.72","chicago":"Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs Distributions.” In 50th International Colloquium on Automata, Languages, and Programming, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.72.","short":"D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ista":"Harris DG, Kolmogorov V. 2023. Parameter estimation for Gibbs distributions. 50th International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming, LIPIcs, vol. 261, 72."},"ddc":["000","510"],"department":[{"_id":"VlKo"}],"file_date_updated":"2023-08-21T06:45:16Z","abstract":[{"lang":"eng","text":"A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We will consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n].\r\nThe partition function is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log Z(β_max))/Z(β_min)\r\nWe develop a number of algorithms to estimate the counts c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²) samples for integer-valued distributions (ignoring some second-order terms and parameters), We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs and perfect matchings in a graph."}],"article_processing_charge":"Yes","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","has_accepted_license":"1","month":"07","date_updated":"2025-07-10T11:50:45Z","publication_status":"published","status":"public","date_created":"2023-08-20T22:01:14Z","conference":{"end_date":"2023-07-14","start_date":"2023-07-10","name":"ICALP: Automata, Languages and Programming","location":"Paderborn, Germany"},"external_id":{"arxiv":["2007.10824"]},"quality_controlled":"1","volume":261,"type":"conference","file":[{"date_created":"2023-08-21T06:45:16Z","success":1,"file_size":917791,"creator":"dernst","access_level":"open_access","checksum":"6dee0684245bb1c524b9c955db1e933d","content_type":"application/pdf","date_updated":"2023-08-21T06:45:16Z","file_id":"14088","file_name":"2023_LIPIcsICALP_Harris.pdf","relation":"main_file"}],"language":[{"iso":"eng"}],"acknowledgement":"We thank Heng Guo for helpful explanations of algorithms for sampling connected subgraphs and matchings, Maksym Serbyn for bringing to our attention the Wang-Landau algorithm and its use in physics.","_id":"14084","oa_version":"Published Version","arxiv":1,"year":"2023","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["9783959772785"],"issn":["1868-8969"]},"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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"related_material":{"record":[{"status":"public","id":"18855","relation":"later_version"}]},"corr_author":"1","fulldoi":"https://doi.org/10.4230/LIPIcs.ICALP.2023.72","date_published":"2023-07-01T00:00:00Z","oa":1,"article_number":"72","title":"Parameter estimation for Gibbs distributions","alternative_title":["LIPIcs"],"day":"01","publication":"50th International Colloquium on Automata, Languages, and Programming"},{"oa_version":"Preprint","_id":"14448","year":"2023","arxiv":1,"language":[{"iso":"eng"}],"volume":2023,"type":"conference","publication":"Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition","title":"Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions","day":"22","fulldoi":"https://doi.org/10.1109/CVPR52729.2023.01153","date_published":"2023-08-22T00:00:00Z","oa":1,"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","publication_identifier":{"isbn":["9798350301298"],"issn":["1063-6919"]},"corr_author":"1","page":"11980-11989","publisher":"IEEE","department":[{"_id":"VlKo"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2010.09567","open_access":"1"}],"abstract":[{"lang":"eng","text":"We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in [16], [35]. As a key computational subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth convex function over a combinatorial polytope. We propose an efficient implementation of this subroutine based on in-face Frank-Wolfe directions, introduced in [4] in a different context. More generally, we define an abstract data structure for a combinatorial subproblem that enables in-face FW directions, and describe its specialization for tree-structured MAP-MRF inference subproblems. Experimental results indicate that the resulting method is the current state-of-art LP solver for some classes of problems. Our code is available at pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html."}],"article_processing_charge":"No","citation":{"ista":"Kolmogorov V. 2023. Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition vol. 2023, 11980–11989.","short":"V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2023, pp. 11980–11989.","mla":"Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial in-Face Frank-Wolfe Directions.” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2023, IEEE, 2023, pp. 11980–89, doi:10.1109/CVPR52729.2023.01153.","chicago":"Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial in-Face Frank-Wolfe Directions.” In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2023:11980–89. IEEE, 2023. https://doi.org/10.1109/CVPR52729.2023.01153.","ieee":"V. Kolmogorov, “Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vancouver, Canada, 2023, vol. 2023, pp. 11980–11989.","apa":"Kolmogorov, V. (2023). Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 2023, pp. 11980–11989). Vancouver, Canada: IEEE. https://doi.org/10.1109/CVPR52729.2023.01153","ama":"Kolmogorov V. Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe directions. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol 2023. IEEE; 2023:11980-11989. doi:10.1109/CVPR52729.2023.01153"},"intvolume":" 2023","doi":"10.1109/CVPR52729.2023.01153","author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov"}],"conference":{"location":"Vancouver, Canada","name":"CVPR: Conference on Computer Vision and Pattern Recognition","start_date":"2023-06-17","end_date":"2023-06-24"},"external_id":{"arxiv":["2010.09567"],"isi":["001062522104029"]},"quality_controlled":"1","status":"public","date_created":"2023-10-22T22:01:16Z","date_updated":"2025-09-09T13:09:58Z","publication_status":"published","month":"08"},{"article_number":"15","title":"Closure properties of general grammars - formally verified","day":"27","alternative_title":["LIPIcs"],"publication":"14th International Conference on Interactive Theorem Proving","publication_identifier":{"isbn":["9783959772846"],"eissn":["1868-8969"]},"scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"corr_author":"1","related_material":{"link":[{"url":"https://github.com/madvorak/grammars/tree/publish","relation":"software"}],"record":[{"status":"public","id":"21393","relation":"dissertation_contains"}]},"fulldoi":"https://doi.org/10.4230/LIPIcs.ITP.2023.15","date_published":"2023-07-27T00:00:00Z","oa":1,"isi":1,"oa_version":"Published Version","_id":"13120","year":"2023","arxiv":1,"volume":268,"file":[{"success":1,"date_created":"2023-08-07T11:55:43Z","relation":"main_file","file_name":"2023_LIPIcS_Dvorak.pdf","date_updated":"2023-08-07T11:55:43Z","file_id":"13982","access_level":"open_access","checksum":"773a0197f05b67feaa6cb1e17ec3642d","content_type":"application/pdf","file_size":715976,"creator":"dernst"}],"type":"conference","language":[{"iso":"eng"}],"acknowledgement":"Jasmin Blanchette: This research has received funding from the Netherlands Organization\r\nfor Scientific Research (NWO) under the Vidi program (project No. 016.Vidi.189.037, Lean Forward).\r\n__\r\nWe thank Vladimir Kolmogorov for making this collaboration possible. We\r\nthank Václav Končický for discussing ideas about the Kleene star construction. We thank Patrick Johnson, Floris van Doorn, and Damiano Testa for their small yet very valuable contributions to our code. We thank Eric Wieser for simplifying one of our proofs. We thank Mark Summerfield for suggesting textual improvements. We thank the anonymous reviewers for very helpful comments. Finally, we thank the Lean community for helping us with various technical issues and answering many questions. ","status":"public","date_created":"2023-06-05T07:29:05Z","conference":{"location":"Bialystok, Poland","end_date":"2023-08-04","start_date":"2023-07-31","name":"ITP: Interactive Theorem Proving"},"external_id":{"isi":["001515590500015"],"arxiv":["2302.06420"]},"quality_controlled":"1","month":"07","date_updated":"2026-07-29T12:56:51Z","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"file_date_updated":"2023-08-07T11:55:43Z","article_processing_charge":"No","abstract":[{"text":"We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant. We defined basic notions of rewrite rules and of words derived by a grammar, and used grammars to show closure of the class of type-0 languages under four operations: union, reversal, concatenation, and the Kleene star. The literature mostly focuses on Turing machine arguments, which are possibly more difficult to formalize. For the Kleene star, we could not follow the literature and came up with our own grammar-based construction.","lang":"eng"}],"has_accepted_license":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","intvolume":" 268","doi":"10.4230/LIPIcs.ITP.2023.15","author":[{"full_name":"Dvorak, Martin","first_name":"Martin","last_name":"Dvorak","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","orcid":"0000-0001-5293-214X"},{"last_name":"Blanchette","first_name":"Jasmin","full_name":"Blanchette, Jasmin"}],"citation":{"mla":"Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” 14th International Conference on Interactive Theorem Proving, vol. 268, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ITP.2023.15.","chicago":"Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars - Formally Verified.” In 14th International Conference on Interactive Theorem Proving, Vol. 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ITP.2023.15.","ieee":"M. Dvorak and J. Blanchette, “Closure properties of general grammars - formally verified,” in 14th International Conference on Interactive Theorem Proving, Bialystok, Poland, 2023, vol. 268.","ama":"Dvorak M, Blanchette J. Closure properties of general grammars - formally verified. In: 14th International Conference on Interactive Theorem Proving. Vol 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ITP.2023.15","apa":"Dvorak, M., & Blanchette, J. (2023). Closure properties of general grammars - formally verified. In 14th International Conference on Interactive Theorem Proving (Vol. 268). Bialystok, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ITP.2023.15","ista":"Dvorak M, Blanchette J. 2023. Closure properties of general grammars - formally verified. 14th International Conference on Interactive Theorem Proving. ITP: Interactive Theorem Proving, LIPIcs, vol. 268, 15.","short":"M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023."},"ddc":["000"]},{"publication_status":"published","date_updated":"2024-10-09T21:01:33Z","issue":"1","month":"01","quality_controlled":"1","external_id":{"arxiv":["1404.5475"],"isi":["000749997700015"]},"date_created":"2022-02-06T23:01:32Z","status":"public","citation":{"short":"R. Takhanov, V. Kolmogorov, Intelligent Data Analysis 26 (2022) 257–272.","ista":"Takhanov R, Kolmogorov V. 2022. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 26(1), 257–272.","ieee":"R. Takhanov and V. Kolmogorov, “Combining pattern-based CRFs and weighted context-free grammars,” Intelligent Data Analysis, vol. 26, no. 1. IOS Press, pp. 257–272, 2022.","apa":"Takhanov, R., & Kolmogorov, V. (2022). Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. IOS Press. https://doi.org/10.3233/IDA-205623","ama":"Takhanov R, Kolmogorov V. Combining pattern-based CRFs and weighted context-free grammars. Intelligent Data Analysis. 2022;26(1):257-272. doi:10.3233/IDA-205623","chicago":"Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and Weighted Context-Free Grammars.” Intelligent Data Analysis. IOS Press, 2022. https://doi.org/10.3233/IDA-205623.","mla":"Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and Weighted Context-Free Grammars.” Intelligent Data Analysis, vol. 26, no. 1, IOS Press, 2022, pp. 257–72, doi:10.3233/IDA-205623."},"author":[{"full_name":"Takhanov, Rustem","first_name":"Rustem","last_name":"Takhanov","id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"}],"doi":"10.3233/IDA-205623","intvolume":" 26","publisher":"IOS Press","article_processing_charge":"No","abstract":[{"text":"We consider two models for the sequence labeling (tagging) problem. The first one is a Pattern-Based Conditional Random Field (PB), in which the energy of a string (chain labeling) x=x1…xn∈Dn is a sum of terms over intervals [i,j] where each term is non-zero only if the substring xi…xj equals a prespecified word w∈Λ. The second model is a Weighted Context-Free Grammar (WCFG) frequently used for natural language processing. PB and WCFG encode local and non-local interactions respectively, and thus can be viewed as complementary. We propose a Grammatical Pattern-Based CRF model (GPB) that combines the two in a natural way. We argue that it has certain advantages over existing approaches such as the Hybrid model of Benedí and Sanchez that combines N-grams and WCFGs. The focus of this paper is to analyze the complexity of inference tasks in a GPB such as computing MAP. We present a polynomial-time algorithm for general GPBs and a faster version for a special case that we call Interaction Grammars.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1404.5475","open_access":"1"}],"department":[{"_id":"VlKo"}],"isi":1,"oa":1,"date_published":"2022-01-14T00:00:00Z","fulldoi":"https://doi.org/10.3233/IDA-205623","corr_author":"1","page":"257-272","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","publication_identifier":{"eissn":["1571-4128"],"issn":["1088-467X"]},"publication":"Intelligent Data Analysis","day":"14","title":"Combining pattern-based CRFs and weighted context-free grammars","language":[{"iso":"eng"}],"type":"journal_article","volume":26,"article_type":"original","arxiv":1,"year":"2022","oa_version":"Preprint","_id":"10737"},{"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"month":"07","ec_funded":1,"publication_status":"published","date_updated":"2026-07-07T05:33:15Z","issue":"4","date_created":"2021-06-06T22:01:30Z","das_tickbox":"1","status":"public","quality_controlled":"1","external_id":{"isi":["000650507600001"]},"author":[{"first_name":"Olaniyi S.","full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola"},{"last_name":"Enyi","first_name":"Cyril D.","full_name":"Enyi, Cyril D."},{"full_name":"Shehu, Yekini","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","last_name":"Shehu"}],"doi":"10.1080/10556788.2021.1924715","intvolume":" 37","citation":{"ista":"Iyiola OS, Enyi CD, Shehu Y. 2022. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 37(4), 1527–1565.","short":"O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software 37 (2022) 1527–1565.","mla":"Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software, vol. 37, no. 4, Taylor & Francis, 2022, pp. 1527–65, doi:10.1080/10556788.2021.1924715.","ieee":"O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” Optimization Methods and Software, vol. 37, no. 4. Taylor & Francis, pp. 1527–1565, 2022.","ama":"Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 2022;37(4):1527-1565. doi:10.1080/10556788.2021.1924715","apa":"Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2022). Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. Taylor & Francis. https://doi.org/10.1080/10556788.2021.1924715","chicago":"Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software. Taylor & Francis, 2022. https://doi.org/10.1080/10556788.2021.1924715."},"abstract":[{"text":"In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"VlKo"}],"publisher":"Taylor & Francis","page":"1527-1565","corr_author":"1","scopus_import":"1","publication_identifier":{"issn":["1055-6788"],"eissn":["1029-4937"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"date_published":"2022-07-01T00:00:00Z","fulldoi":"https://doi.org/10.1080/10556788.2021.1924715","day":"01","title":"Reflected three-operator splitting method for monotone inclusion problem","publication":"Optimization Methods and Software","type":"journal_article","volume":37,"acknowledgement":"The authors are grateful to the anonymous referees and the handling Editor for their insightful comments which have improved the earlier version of the manuscript greatly. The second author is grateful to the University of Hafr Al Batin. The last 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).","language":[{"iso":"eng"}],"year":"2022","_id":"9469","oa_version":"None","article_type":"original"},{"oa_version":"None","_id":"9365","year":"2022","article_type":"original","type":"journal_article","volume":71,"acknowledgement":"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).","language":[{"iso":"eng"}],"day":"01","title":"Convergence analysis of new inertial method for the split common null point problem","publication":"Optimization","page":"3767-3795","publication_identifier":{"issn":["0233-1934"],"eissn":["1029-4945"]},"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"fulldoi":"https://doi.org/10.1080/02331934.2021.1914035","date_published":"2022-11-01T00:00:00Z","abstract":[{"text":"In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"VlKo"}],"publisher":"Taylor & Francis","author":[{"full_name":"Ogbuisi, Ferdinard U.","first_name":"Ferdinard U.","last_name":"Ogbuisi"},{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","last_name":"Shehu","full_name":"Shehu, Yekini","first_name":"Yekini"},{"last_name":"Yao","full_name":"Yao, Jen Chih","first_name":"Jen Chih"}],"intvolume":" 71","doi":"10.1080/02331934.2021.1914035","citation":{"ieee":"F. U. Ogbuisi, Y. Shehu, and J. C. Yao, “Convergence analysis of new inertial method for the split common null point problem,” Optimization, vol. 71, no. 13. Taylor & Francis, pp. 3767–3795, 2022.","apa":"Ogbuisi, F. U., Shehu, Y., & Yao, J. C. (2022). Convergence analysis of new inertial method for the split common null point problem. Optimization. Taylor & Francis. https://doi.org/10.1080/02331934.2021.1914035","ama":"Ogbuisi FU, Shehu Y, Yao JC. Convergence analysis of new inertial method for the split common null point problem. Optimization. 2022;71(13):3767-3795. doi:10.1080/02331934.2021.1914035","chicago":"Ogbuisi, Ferdinard U., Yekini Shehu, and Jen Chih Yao. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization. Taylor & Francis, 2022. https://doi.org/10.1080/02331934.2021.1914035.","mla":"Ogbuisi, Ferdinard U., et al. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization, vol. 71, no. 13, Taylor & Francis, 2022, pp. 3767–95, doi:10.1080/02331934.2021.1914035.","ista":"Ogbuisi FU, Shehu Y, Yao JC. 2022. Convergence analysis of new inertial method for the split common null point problem. Optimization. 71(13), 3767–3795.","short":"F.U. Ogbuisi, Y. Shehu, J.C. Yao, Optimization 71 (2022) 3767–3795."},"das_tickbox":"1","date_created":"2021-05-02T22:01:29Z","status":"public","quality_controlled":"1","external_id":{"isi":["000640109300001"]},"project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"month":"11","ec_funded":1,"publication_status":"published","issue":"13","date_updated":"2026-07-07T05:32:47Z"},{"ddc":["510","515","518"],"citation":{"chicago":"Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor & Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287.","apa":"Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287","ieee":"Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor & Francis, pp. 192–216, 2022.","ama":"Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287","mla":"Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor & Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287.","short":"Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216.","ista":"Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216."},"author":[{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","last_name":"Shehu","full_name":"Shehu, Yekini","first_name":"Yekini"},{"last_name":"Iyiola","first_name":"Olaniyi S.","full_name":"Iyiola, Olaniyi S."}],"doi":"10.1080/00036811.2020.1736287","intvolume":" 101","publisher":"Taylor & Francis","has_accepted_license":"1","article_processing_charge":"No","abstract":[{"text":"Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods.","lang":"eng"}],"file_date_updated":"2021-03-16T23:30:06Z","department":[{"_id":"VlKo"}],"publication_status":"published","date_updated":"2024-11-04T13:52:44Z","issue":"1","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"}],"ec_funded":1,"month":"01","quality_controlled":"1","external_id":{"isi":["000518364100001"],"arxiv":["2101.08057"]},"date_created":"2020-03-09T07:06:52Z","status":"public","acknowledgement":"The project of the first 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).","language":[{"iso":"eng"}],"type":"journal_article","file":[{"date_created":"2020-10-12T10:42:54Z","creator":"dernst","file_size":4282586,"embargo":"2021-03-15","content_type":"application/pdf","checksum":"869efe8cb09505dfa6012f67d20db63d","access_level":"open_access","file_id":"8648","date_updated":"2021-03-16T23:30:06Z","relation":"main_file","file_name":"2020_ApplicAnalysis_Shehu.pdf"}],"volume":101,"article_type":"original","year":"2022","arxiv":1,"oa_version":"Submitted Version","_id":"7577","isi":1,"oa":1,"date_published":"2022-01-01T00:00:00Z","fulldoi":"https://doi.org/10.1080/00036811.2020.1736287","corr_author":"1","page":"192-216","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1563-504X"],"issn":["0003-6811"]},"scopus_import":"1","publication":"Applicable Analysis","day":"01","title":"Weak convergence for variational inequalities with inertial-type method"},{"oa_version":"Published Version","_id":"10072","year":"2021","arxiv":1,"type":"conference","file":[{"creator":"cchlebak","file_size":804472,"content_type":"application/pdf","checksum":"9d2544d53aa5b01565c6891d97a4d765","access_level":"open_access","file_id":"10098","date_updated":"2021-10-06T13:51:54Z","relation":"main_file","file_name":"2021_LIPIcs_Harris.pdf","date_created":"2021-10-06T13:51:54Z","success":1}],"volume":207,"acknowledgement":"Fotis Iliopoulos: This material is based upon work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the National Science Foundation Grant No. CCF-1815328.\r\nVladimir Kolmogorov: Supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160.","language":[{"iso":"eng"}],"day":"15","alternative_title":["LIPIcs"],"article_number":"31","title":"A new notion of commutativity for the algorithmic Lovász Local Lemma","publication":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"related_material":{"record":[{"id":"21143","relation":"later_version","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["978-3-9597-7207-5"],"issn":["1868-8969"]},"scopus_import":"1","oa":1,"fulldoi":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31","date_published":"2021-09-15T00:00:00Z","abstract":[{"text":"The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works revealed that the LLL has intimate connections with a class of stochastic local search algorithms for finding such desirable objects. In particular, it can be seen as a sufficient condition for this type of algorithms to converge fast. Besides conditions for existence of and fast convergence to desirable objects, one may naturally ask further questions regarding properties of these algorithms. For instance, \"are they parallelizable?\", \"how many solutions can they output?\", \"what is the expected \"weight\" of a solution?\", etc. These questions and more have been answered for a class of LLL-inspired algorithms called commutative. In this paper we introduce a new, very natural and more general notion of commutativity (essentially matrix commutativity) which allows us to show a number of new refined properties of LLL-inspired local search algorithms with significantly simpler proofs.","lang":"eng"}],"article_processing_charge":"Yes","file_date_updated":"2021-10-06T13:51:54Z","department":[{"_id":"VlKo"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","has_accepted_license":"1","author":[{"last_name":"Harris","full_name":"Harris, David G.","first_name":"David G."},{"last_name":"Iliopoulos","first_name":"Fotis","full_name":"Iliopoulos, Fotis"},{"first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov"}],"intvolume":" 207","doi":"10.4230/LIPIcs.APPROX/RANDOM.2021.31","ddc":["000"],"citation":{"ista":"Harris DG, Iliopoulos F, Kolmogorov V. 2021. A new notion of commutativity for the algorithmic Lovász Local Lemma. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation, LIPIcs, vol. 207, 31.","short":"D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","mla":"Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, vol. 207, 31, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31.","chicago":"Harris, David G., Fotis Iliopoulos, and Vladimir Kolmogorov. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Vol. 207. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31.","apa":"Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2021). A new notion of commutativity for the algorithmic Lovász Local Lemma. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Vol. 207). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31","ieee":"D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity for the algorithmic Lovász Local Lemma,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Virtual, 2021, vol. 207.","ama":"Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the algorithmic Lovász Local Lemma. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Vol 207. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31"},"date_created":"2021-10-03T22:01:22Z","status":"public","quality_controlled":"1","conference":{"location":"Virtual","end_date":"2021-08-18","name":"APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation","start_date":"2021-08-16"},"external_id":{"arxiv":["2008.05569"]},"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"month":"09","ec_funded":1,"publication_status":"published","date_updated":"2026-02-10T09:59:59Z"},{"main_file_link":[{"url":"https://arxiv.org/abs/2101.12617","open_access":"1"}],"abstract":[{"text":"We study a class of convex-concave saddle-point problems of the form minxmaxy⟨Kx,y⟩+fP(x)−h∗(y) where K is a linear operator, fP is the sum of a convex function f with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope P, and h∗ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle (lmo) for fP and an efficient proximal map for h∗ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case h∗ is the indicator function of a linear constraint and function f is quadratic, we show a O(1/n2) convergence rate on the dual objective, requiring O(nlogn) calls of lmo. If the problem comes from the constrained optimization problem minx∈Rd{fP(x)|Ax−b=0} then we additionally get bound O(1/n2) both on the primal gap and on the infeasibility gap. In the most general case, we show a O(1/n) convergence rate of the primal-dual gap again requiring O(nlogn) calls of lmo. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"VlKo"}],"citation":{"ista":"Kolmogorov V, Pock T. 2021. One-sided Frank-Wolfe algorithms for saddle problems. 38th International Conference on Machine Learning. ICML: International Conference on Machine Learning.","short":"V. Kolmogorov, T. Pock, in:, 38th International Conference on Machine Learning, 2021.","apa":"Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for saddle problems. In 38th International Conference on Machine Learning. Virtual.","ama":"Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems. In: 38th International Conference on Machine Learning. ; 2021.","ieee":"V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,” in 38th International Conference on Machine Learning, Virtual, 2021.","chicago":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” In 38th International Conference on Machine Learning, 2021.","mla":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” 38th International Conference on Machine Learning, 2021."},"author":[{"last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir"},{"last_name":"Pock","full_name":"Pock, Thomas","first_name":"Thomas"}],"quality_controlled":"1","external_id":{"arxiv":["2101.12617"]},"conference":{"location":"Virtual","end_date":"2021-07-24","name":"ICML: International Conference on Machine Learning","start_date":"2021-07-18"},"date_created":"2021-12-16T12:41:20Z","status":"public","publication_status":"published","date_updated":"2025-07-16T08:04:23Z","project":[{"call_identifier":"FP7","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"month":"07","ec_funded":1,"year":"2021","arxiv":1,"oa_version":"Preprint","_id":"10552","acknowledgement":"Vladimir Kolmogorov was supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160. Thomas Pock acknowledges support by an ERC grant HOMOVIS, no 640156.","language":[{"iso":"eng"}],"type":"conference","publication":"38th International Conference on Machine Learning","day":"01","title":"One-sided Frank-Wolfe algorithms for saddle problems","oa":1,"date_published":"2021-07-01T00:00:00Z","corr_author":"1","scopus_import":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"date_updated":"2024-11-04T13:52:35Z","publication_status":"published","month":"09","ec_funded":1,"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"external_id":{"isi":["000537342300001"]},"quality_controlled":"1","status":"public","date_created":"2020-06-04T11:28:33Z","citation":{"short":"Y. Shehu, A. Gibali, Optimization Letters 15 (2021) 2109–2126.","ista":"Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities. Optimization Letters. 15, 2109–2126.","mla":"Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters, vol. 15, Springer Nature, 2021, pp. 2109–26, doi:10.1007/s11590-020-01603-1.","chicago":"Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters. Springer Nature, 2021. https://doi.org/10.1007/s11590-020-01603-1.","ama":"Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities. Optimization Letters. 2021;15:2109-2126. doi:10.1007/s11590-020-01603-1","ieee":"Y. Shehu and A. Gibali, “New inertial relaxed method for solving split feasibilities,” Optimization Letters, vol. 15. Springer Nature, pp. 2109–2126, 2021.","apa":"Shehu, Y., & Gibali, A. (2021). New inertial relaxed method for solving split feasibilities. Optimization Letters. Springer Nature. https://doi.org/10.1007/s11590-020-01603-1"},"ddc":["510"],"doi":"10.1007/s11590-020-01603-1","intvolume":" 15","author":[{"first_name":"Yekini","full_name":"Shehu, Yekini","last_name":"Shehu","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Gibali","full_name":"Gibali, Aviv","first_name":"Aviv"}],"publisher":"Springer Nature","has_accepted_license":"1","file_date_updated":"2024-03-07T14:58:51Z","department":[{"_id":"VlKo"}],"abstract":[{"text":"In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","date_published":"2021-09-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s11590-020-01603-1","isi":1,"oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1862-4480"],"issn":["1862-4472"]},"scopus_import":"1","page":"2109-2126","corr_author":"1","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication":"Optimization Letters","title":"New inertial relaxed method for solving split feasibilities","day":"01","language":[{"iso":"eng"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are grateful to the referees for their insightful comments 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’s Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160).","volume":15,"file":[{"date_created":"2024-03-07T14:58:51Z","success":1,"checksum":"63c5f31cd04626152a19f97a2476281b","access_level":"open_access","content_type":"application/pdf","file_size":2148882,"creator":"kschuh","file_name":"2021_OptimizationLetters_Shehu.pdf","relation":"main_file","date_updated":"2024-03-07T14:58:51Z","file_id":"15089"}],"type":"journal_article","article_type":"original","year":"2021","_id":"7925","oa_version":"Published Version"},{"publisher":"Springer Nature","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","abstract":[{"lang":"eng","text":"This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis."}],"department":[{"_id":"VlKo"}],"file_date_updated":"2020-08-03T15:24:39Z","ddc":["510"],"citation":{"mla":"Shehu, Yekini, et al. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering, vol. 22, Springer Nature, 2021, pp. 2627–53, doi:10.1007/s11081-020-09544-5.","apa":"Shehu, Y., Dong, Q.-L., Liu, L.-L., & Yao, J.-C. (2021). New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. Springer Nature. https://doi.org/10.1007/s11081-020-09544-5","ama":"Shehu Y, Dong Q-L, Liu L-L, Yao J-C. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 2021;22:2627-2653. doi:10.1007/s11081-020-09544-5","ieee":"Y. Shehu, Q.-L. Dong, L.-L. Liu, and J.-C. Yao, “New strong convergence method for the sum of two maximal monotone operators,” Optimization and Engineering, vol. 22. Springer Nature, pp. 2627–2653, 2021.","chicago":"Shehu, Yekini, Qiao-Li Dong, Lu-Lu Liu, and Jen-Chih Yao. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering. Springer Nature, 2021. https://doi.org/10.1007/s11081-020-09544-5.","ista":"Shehu Y, Dong Q-L, Liu L-L, Yao J-C. 2021. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 22, 2627–2653.","short":"Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering 22 (2021) 2627–2653."},"author":[{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","last_name":"Shehu","full_name":"Shehu, Yekini","first_name":"Yekini"},{"last_name":"Dong","full_name":"Dong, Qiao-Li","first_name":"Qiao-Li"},{"full_name":"Liu, Lu-Lu","first_name":"Lu-Lu","last_name":"Liu"},{"first_name":"Jen-Chih","full_name":"Yao, Jen-Chih","last_name":"Yao"}],"doi":"10.1007/s11081-020-09544-5","intvolume":" 22","quality_controlled":"1","external_id":{"isi":["000559345400001"]},"date_created":"2020-08-03T14:29:57Z","status":"public","publication_status":"published","date_updated":"2024-11-04T13:52:38Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"ec_funded":1,"month":"02","article_type":"original","year":"2021","_id":"8196","oa_version":"Published Version","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7—2007–2013) (Grant Agreement No. 616160). The authors are grateful to the anonymous referees and the handling Editor for their comments and suggestions which have improved the earlier version of the manuscript greatly.","language":[{"iso":"eng"}],"type":"journal_article","file":[{"date_created":"2020-08-03T15:24:39Z","success":1,"creator":"dernst","file_size":2137860,"content_type":"application/pdf","access_level":"open_access","file_id":"8197","date_updated":"2020-08-03T15:24:39Z","relation":"main_file","file_name":"2020_OptimizationEngineering_Shehu.pdf"}],"volume":22,"publication":"Optimization and Engineering","day":"25","title":"New strong convergence method for the sum of two maximal monotone operators","isi":1,"oa":1,"date_published":"2021-02-25T00:00:00Z","fulldoi":"https://doi.org/10.1007/s11081-020-09544-5","corr_author":"1","page":"2627-2653","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","publication_identifier":{"eissn":["1573-2924"],"issn":["1389-4420"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"abstract":[{"text":"The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"VlKo"}],"publisher":"Springer Nature","author":[{"last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","first_name":"Yekini"},{"full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S.","last_name":"Iyiola"},{"first_name":"Duong Viet","full_name":"Thong, Duong Viet","last_name":"Thong"},{"first_name":"Nguyen Thi Cam","full_name":"Van, Nguyen Thi Cam","last_name":"Van"}],"intvolume":" 93","doi":"10.1007/s00186-020-00730-w","citation":{"mla":"Shehu, Yekini, et al. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research, vol. 93, no. 2, Springer Nature, 2021, pp. 213–42, doi:10.1007/s00186-020-00730-w.","chicago":"Shehu, Yekini, Olaniyi S. Iyiola, Duong Viet Thong, and Nguyen Thi Cam Van. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research. Springer Nature, 2021. https://doi.org/10.1007/s00186-020-00730-w.","ama":"Shehu Y, Iyiola OS, Thong DV, Van NTC. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 2021;93(2):213-242. doi:10.1007/s00186-020-00730-w","ieee":"Y. Shehu, O. S. Iyiola, D. V. Thong, and N. T. C. Van, “An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems,” Mathematical Methods of Operations Research, vol. 93, no. 2. Springer Nature, pp. 213–242, 2021.","apa":"Shehu, Y., Iyiola, O. S., Thong, D. V., & Van, N. T. C. (2021). An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. Springer Nature. https://doi.org/10.1007/s00186-020-00730-w","ista":"Shehu Y, Iyiola OS, Thong DV, Van NTC. 2021. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 93(2), 213–242.","short":"Y. Shehu, O.S. Iyiola, D.V. Thong, N.T.C. Van, Mathematical Methods of Operations Research 93 (2021) 213–242."},"date_created":"2020-11-29T23:01:18Z","status":"public","quality_controlled":"1","external_id":{"isi":["000590497300001"]},"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"month":"04","ec_funded":1,"publication_status":"published","issue":"2","date_updated":"2024-11-04T13:52:33Z","oa_version":"None","_id":"8817","year":"2021","article_type":"original","type":"journal_article","volume":93,"acknowledgement":"The authors are grateful to the two referees and the Associate Editor for their comments and suggestions which have improved the earlier version of the paper greatly. The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160).","language":[{"iso":"eng"}],"day":"01","title":"An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems","publication":"Mathematical Methods of Operations Research","page":"213-242","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","publication_identifier":{"issn":["1432-2994"],"eissn":["1432-5217"]},"isi":1,"fulldoi":"https://doi.org/10.1007/s00186-020-00730-w","date_published":"2021-04-01T00:00:00Z"},{"month":"01","publication_status":"published","date_updated":"2025-09-10T10:01:54Z","date_created":"2021-03-07T23:01:25Z","status":"public","quality_controlled":"1","conference":{"end_date":"2021-02-13","start_date":"2021-02-11","name":"CALDAM: Conference on Algorithms and Discrete Applied Mathematics","location":"Rupnagar, India"},"external_id":{"isi":["001433483100028"]},"author":[{"first_name":"Andrew","full_name":"Bloch-Hansen, Andrew","last_name":"Bloch-Hansen"},{"id":"C1531CAE-36E9-11EA-845F-33AA3DDC885E","last_name":"Samei","first_name":"Nasim","full_name":"Samei, Nasim"},{"first_name":"Roberto","full_name":"Solis-Oba, Roberto","last_name":"Solis-Oba"}],"intvolume":" 12601","doi":"10.1007/978-3-030-67899-9_28","citation":{"mla":"Bloch-Hansen, Andrew, et al. “Experimental Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem.” Conference on Algorithms and Discrete Applied Mathematics, vol. 12601, Springer Nature, 2021, pp. 346–58, doi:10.1007/978-3-030-67899-9_28.","apa":"Bloch-Hansen, A., Samei, N., & Solis-Oba, R. (2021). Experimental evaluation of a local search approximation algorithm for the multiway cut problem. In Conference on Algorithms and Discrete Applied Mathematics (Vol. 12601, pp. 346–358). Rupnagar, India: Springer Nature. https://doi.org/10.1007/978-3-030-67899-9_28","ama":"Bloch-Hansen A, Samei N, Solis-Oba R. Experimental evaluation of a local search approximation algorithm for the multiway cut problem. In: Conference on Algorithms and Discrete Applied Mathematics. Vol 12601. Springer Nature; 2021:346-358. doi:10.1007/978-3-030-67899-9_28","ieee":"A. Bloch-Hansen, N. Samei, and R. Solis-Oba, “Experimental evaluation of a local search approximation algorithm for the multiway cut problem,” in Conference on Algorithms and Discrete Applied Mathematics, Rupnagar, India, 2021, vol. 12601, pp. 346–358.","chicago":"Bloch-Hansen, Andrew, Nasim Samei, and Roberto Solis-Oba. “Experimental Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem.” In Conference on Algorithms and Discrete Applied Mathematics, 12601:346–58. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-67899-9_28.","ista":"Bloch-Hansen A, Samei N, Solis-Oba R. 2021. Experimental evaluation of a local search approximation algorithm for the multiway cut problem. Conference on Algorithms and Discrete Applied Mathematics. CALDAM: Conference on Algorithms and Discrete Applied Mathematics, LNCS, vol. 12601, 346–358.","short":"A. Bloch-Hansen, N. Samei, R. Solis-Oba, in:, Conference on Algorithms and Discrete Applied Mathematics, Springer Nature, 2021, pp. 346–358."},"article_processing_charge":"No","abstract":[{"lang":"eng","text":"In the multiway cut problem we are given a weighted undirected graph G=(V,E) and a set T⊆V of k terminals. The goal is to find a minimum weight set of edges E′⊆E with the property that by removing E′ from G all the terminals become disconnected. In this paper we present a simple local search approximation algorithm for the multiway cut problem with approximation ratio 2−2k . We present an experimental evaluation of the performance of our local search algorithm and show that it greatly outperforms the isolation heuristic of Dalhaus et al. and it has similar performance as the much more complex algorithms of Calinescu et al., Sharma and Vondrak, and Buchbinder et al. which have the currently best known approximation ratios for this problem."}],"department":[{"_id":"VlKo"}],"publisher":"Springer Nature","page":"346-358","publication_identifier":{"issn":["0302-9743"],"isbn":["9783030678982"],"eissn":["1611-3349"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","isi":1,"fulldoi":"https://doi.org/10.1007/978-3-030-67899-9_28","date_published":"2021-01-28T00:00:00Z","day":"28","alternative_title":["LNCS"],"title":"Experimental evaluation of a local search approximation algorithm for the multiway cut problem","publication":"Conference on Algorithms and Discrete Applied Mathematics","type":"conference","volume":12601,"language":[{"iso":"eng"}],"oa_version":"None","_id":"9227","year":"2021"},{"status":"public","date_created":"2021-03-10T12:18:47Z","external_id":{"isi":["000625002100001"]},"quality_controlled":"1","ec_funded":1,"month":"06","project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"issue":"2","date_updated":"2024-11-04T13:52:33Z","publication_status":"published","file_date_updated":"2021-08-11T12:44:16Z","department":[{"_id":"VlKo"}],"abstract":[{"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.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","publisher":"Springer Nature","intvolume":" 21","doi":"10.1007/s11067-021-09517-w","author":[{"full_name":"Izuchukwu, Chinedu","first_name":"Chinedu","last_name":"Izuchukwu"},{"full_name":"Shehu, Yekini","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","last_name":"Shehu"}],"citation":{"short":"C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323.","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. Networks and Spatial Economics. 2021;21(2):291-323. doi:10.1007/s11067-021-09517-w","ieee":"C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity,” Networks and Spatial Economics, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021.","apa":"Izuchukwu, C., & Shehu, Y. (2021). New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. Springer Nature. https://doi.org/10.1007/s11067-021-09517-w","chicago":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks and Spatial Economics. Springer Nature, 2021. https://doi.org/10.1007/s11067-021-09517-w.","mla":"Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks and Spatial Economics, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323, doi:10.1007/s11067-021-09517-w."},"ddc":["510"],"title":"New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity","day":"01","publication":"Networks and Spatial Economics","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"eissn":["1572-9427"],"issn":["1566-113X"]},"scopus_import":"1","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","image":"/images/cc_by.png","short":"CC BY (4.0)"},"page":"291-323","fulldoi":"https://doi.org/10.1007/s11067-021-09517-w","date_published":"2021-06-01T00:00:00Z","oa":1,"isi":1,"_id":"9234","oa_version":"Published Version","year":"2021","keyword":["Computer Networks and Communications","Software","Artificial Intelligence"],"article_type":"original","volume":21,"type":"journal_article","file":[{"date_created":"2021-08-11T12:44:16Z","success":1,"checksum":"22b4253a2e5da843622a2df713784b4c","access_level":"open_access","content_type":"application/pdf","file_size":834964,"creator":"kschuh","relation":"main_file","file_name":"2021_NetworksSpatialEconomics_Shehu.pdf","date_updated":"2021-08-11T12:44:16Z","file_id":"9884"}],"language":[{"iso":"eng"}],"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)."},{"status":"public","date_created":"2021-04-11T22:01:14Z","external_id":{"isi":["000632917700001"]},"quality_controlled":"1","month":"03","issue":"2","date_updated":"2024-10-09T21:00:33Z","publication_status":"published","department":[{"_id":"VlKo"}],"article_processing_charge":"No","abstract":[{"lang":"eng","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."}],"publisher":"Springer Nature","intvolume":" 76","doi":"10.1007/s00025-021-01381-x","author":[{"last_name":"Iyiola","full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S."},{"orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini","full_name":"Shehu, Yekini"}],"citation":{"short":"O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021).","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.","mla":"Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results in Mathematics, vol. 76, no. 2, 75, Springer Nature, 2021, doi:10.1007/s00025-021-01381-x.","chicago":"Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results in Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s00025-021-01381-x.","ama":"Iyiola OS, Shehu Y. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 2021;76(2). doi:10.1007/s00025-021-01381-x","apa":"Iyiola, O. S., & Shehu, Y. (2021). New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. Springer Nature. https://doi.org/10.1007/s00025-021-01381-x","ieee":"O. S. Iyiola and Y. Shehu, “New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications,” Results in Mathematics, vol. 76, no. 2. Springer Nature, 2021."},"article_number":"75","title":"New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications","day":"25","publication":"Results in Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","publication_identifier":{"issn":["1422-6383"],"eissn":["1420-9012"]},"corr_author":"1","fulldoi":"https://doi.org/10.1007/s00025-021-01381-x","date_published":"2021-03-25T00:00:00Z","isi":1,"_id":"9315","oa_version":"None","year":"2021","article_type":"original","volume":76,"type":"journal_article","language":[{"iso":"eng"}],"acknowledgement":"The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria."}]