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This article is cited in 44 scientific papers (total in 44 papers)
Universal method for stochastic composite optimization problems
A. V. Gasnikovab, Yu. E. Nesterovcd a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, Russia
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
c National Research University Higher School of Economics, Moscow, Russia
d Louvain-la-Neuve, Belgium
Abstract:
A fast gradient method requiring only one projection is proposed for smooth convex optimization problems. The method has a visual geometric interpretation, so it is called the method of similar triangles (MST). Composite, adaptive, and universal versions of MST are suggested. Based on MST, a universal method is proposed for the first time for strongly convex problems (this method is continuous with respect to the strong convexity parameter of the smooth part of the functional). It is shown how the universal version of MST can be applied to stochastic optimization problems.
Key words:
fast gradient method, composite optimization, universal method, strongly convex case, stochastic optimization, method of similar triangles.
Received: 12.05.2016 Revised: 28.08.2016
Citation:
A. V. Gasnikov, Yu. E. Nesterov, “Universal method for stochastic composite optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 58:1 (2018), 52–69; Comput. Math. Math. Phys., 58:1 (2018), 48–64
Linking options:
https://www.mathnet.ru/eng/zvmmf10659 https://www.mathnet.ru/eng/zvmmf/v58/i1/p52
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