Email this article Universal Method for Stochastic Composite Optimization Problems
- Authors: Gasnikov A.V.1,2, Nesterov Y.E.3,4
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Affiliations:
- Institute for Information Transmission Problems
- Moscow Institute of Physics and Technology
- National Research University Higher School of Economics
- Aff4
- Issue: Vol 58, No 1 (2018)
- Pages: 48-64
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/179966
- DOI: https://doi.org/10.1134/S0965542518010050
- ID: 179966
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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.
About the authors
A. V. Gasnikov
Institute for Information Transmission Problems; Moscow Institute of Physics and Technology
Author for correspondence.
Email: gasnikov.av@mipt.ru
Russian Federation, Moscow, 127051; Dolgoprudnyi, Moscow oblast, 141700
Yu. E. Nesterov
National Research University Higher School of Economics; Aff4
Email: gasnikov.av@mipt.ru
Russian Federation, Moscow, 101000; Voie du Roman Pays 34, Louvain-la-Neuve, L1.03.01–B-1348
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