Primal-dual proximal bundle and conditional gradient methods for convex problems
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| Publicat a: | arXiv.org (Dec 23, 2024), p. n/a |
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| Autor principal: | |
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Cornell University Library, arXiv.org
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| Matèries: | |
| Accés en línia: | Citation/Abstract Full text outside of ProQuest |
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| Resum: | This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for solving convex nonsmooth composite optimization problems and establish the iteration-complexity in terms of a primal-dual gap. We also propose a class of proximal bundle methods for solving convex-concave nonsmooth composite saddle-point problems and establish the iteration-complexity to find an approximate saddle-point. This paper places special emphasis on the primal-dual perspective of the proximal bundle method. In particular, we discover an interesting duality between the conditional gradient method and the cutting-plane scheme used within the proximal bundle method. Leveraging this duality, we further develop novel variants of both the conditional gradient method and the cutting-plane scheme. |
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| ISSN: | 2331-8422 |
| Font: | Engineering Database |