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- W3013562136 abstract "This paper presents a proximal bundle variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Like other proximal bundle variants, RPB solves a sequence of prox bundle subproblems whose objective functions are regularized composite cutting-plane models. Moreover, RPB uses a novel condition to decide whether to perform a serious or null iteration which does not necessarily yield a function value decrease. Optimal iteration-complexity bounds for RPB are established for a large range of prox stepsizes, both in the convex and strongly convex settings. To the best of our knowledge, this is the first time that a proximal bundle variant is shown to be optimal for a large range of prox stepsizes. Finally, iteration-complexity results for RPB to obtain iterates satisfying practical termination criteria, rather than near optimal solutions, are also derived." @default.
- W3013562136 created "2020-04-03" @default.
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- W3013562136 date "2020-03-25" @default.
- W3013562136 modified "2023-09-23" @default.
- W3013562136 title "A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizes" @default.
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- W3013562136 doi "https://doi.org/10.48550/arxiv.2003.11457" @default.
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