{"abstract":[{"lang":"eng","text":"We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal O(1/k−−√) convergence rate. We demonstrate that the same rate holds if the linear subproblems are solved approximately with additive or multiplicative error. In contrast with the relevant work, we are able to characterize the convergence when the non-smooth term is an indicator function. Specific applications of our framework include the non-smooth minimization, semidefinite programming, and minimization with linear inclusion constraints over a compact domain. Numerical evidence demonstrates the benefits of our framework."}],"oa":1,"year":"2018","author":[{"first_name":"Alp","last_name":"Yurtsever","full_name":"Yurtsever, Alp"},{"first_name":"Olivier","last_name":"Fercoq","full_name":"Fercoq, Olivier"},{"last_name":"Locatello","orcid":"0000-0002-4850-0683","first_name":"Francesco","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","full_name":"Locatello, Francesco"},{"full_name":"Cevher, Volkan","first_name":"Volkan","last_name":"Cevher"}],"day":"15","language":[{"iso":"eng"}],"page":"5727-5736","main_file_link":[{"url":"https://arxiv.org/abs/1804.08544","open_access":"1"}],"citation":{"apa":"Yurtsever, A., Fercoq, O., Locatello, F., &#38; Cevher, V. (2018). A conditional gradient framework for composite convex minimization with applications to semidefinite programming. In <i>Proceedings of the 35th International Conference on Machine Learning</i> (Vol. 80, pp. 5727–5736). Stockholm, Sweden: ML Research Press.","ama":"Yurtsever A, Fercoq O, Locatello F, Cevher V. A conditional gradient framework for composite convex minimization with applications to semidefinite programming. In: <i>Proceedings of the 35th International Conference on Machine Learning</i>. Vol 80. ML Research Press; 2018:5727-5736.","chicago":"Yurtsever, Alp, Olivier Fercoq, Francesco Locatello, and Volkan Cevher. “A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming.” In <i>Proceedings of the 35th International Conference on Machine Learning</i>, 80:5727–36. ML Research Press, 2018.","short":"A. Yurtsever, O. Fercoq, F. Locatello, V. Cevher, in:, Proceedings of the 35th International Conference on Machine Learning, ML Research Press, 2018, pp. 5727–5736.","ieee":"A. Yurtsever, O. Fercoq, F. Locatello, and V. Cevher, “A conditional gradient framework for composite convex minimization with applications to semidefinite programming,” in <i>Proceedings of the 35th International Conference on Machine Learning</i>, Stockholm, Sweden, 2018, vol. 80, pp. 5727–5736.","ista":"Yurtsever A, Fercoq O, Locatello F, Cevher V. 2018. A conditional gradient framework for composite convex minimization with applications to semidefinite programming. Proceedings of the 35th International Conference on Machine Learning. ICML: International Conference on Machine Learning, PMLR, vol. 80, 5727–5736.","mla":"Yurtsever, Alp, et al. “A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming.” <i>Proceedings of the 35th International Conference on Machine Learning</i>, vol. 80, ML Research Press, 2018, pp. 5727–36."},"title":"A conditional gradient framework for composite convex minimization with applications to semidefinite programming","intvolume":"        80","article_processing_charge":"No","volume":80,"date_published":"2018-07-15T00:00:00Z","quality_controlled":"1","month":"07","date_created":"2023-08-22T14:16:01Z","alternative_title":["PMLR"],"publication_status":"published","publisher":"ML Research Press","external_id":{"arxiv":["1804.08544"]},"publication":"Proceedings of the 35th International Conference on Machine Learning","department":[{"_id":"FrLo"}],"oa_version":"Preprint","date_updated":"2023-09-13T08:13:39Z","type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"location":"Stockholm, Sweden","end_date":"2018-07-15","start_date":"2018-07-10","name":"ICML: International Conference on Machine Learning"},"status":"public","_id":"14203","extern":"1"}