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

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 1, Pages 52–69
DOI: https://doi.org/10.7868/S0044466918010052 (Mi zvmmf10659)

This article is cited in 44 scientific papers (total in 44 papers)

Universal method for stochastic composite optimization problems

A. V. Gasnikov^ab, Yu. E. Nesterov^cd

^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

Citations (44)

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DOI: https://doi.org/10.7868/S0044466918010052

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.

Funding agency	Grant number
Russian Science Foundation	17-11-01027
Russian Foundation for Basic Research	15-31-70001_мол_а_мос 15-31-20571_мол_а_вед

Received: 12.05.2016
Revised: 28.08.2016

English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 1, Pages 48–64
DOI: https://doi.org/10.1134/S0965542518010050

Bibliographic databases:

Document Type: Article

UDC: 519.626

Language: Russian

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

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This publication is cited in the following 44 articles:

Xuexue Zhang, Sanyang Liu, Nannan Zhao, “An accelerated decentralized stochastic optimization algorithm with inexact model”, Journal of Computational and Applied Mathematics, 459 (2025), 116383
I. V. Podlipnova, Yu. V. Dorn, I. A. Sklonin, “Oblachnaya interpretatsiya entropiinoi modeli rascheta matritsy korrespondentsii”, Kompyuternye issledovaniya i modelirovanie, 16:1 (2024), 89–103
Meruza Kubentayeva, Demyan Yarmoshik, Mikhail Persiianov, Alexey Kroshnin, Ekaterina Kotliarova, Nazarii Tupitsa, Dmitry Pasechnyuk, Alexander Gasnikov, Vladimir Shvetsov, Leonid Baryshev, Alexey Shurupov, “Primal-dual gradient methods for searching network equilibria in combined models with nested choice structure and capacity constraints”, Comput Manag Sci, 21:1 (2024)
Jelena Diakonikolas, Cristóbal Guzmán, “Complementary composite minimization, small gradients in general norms, and applications”, Math. Program., 2024
S. S. Ablaev, A. N. Beznosikov, A. V. Gasnikov, D. M. Dvinskikh, A. V. Lobanov, S. M. Puchinin, F. S. Stonyakin, “On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development”, Comput. Math. and Math. Phys., 64:4 (2024), 635
Vladimir Solodkin, Savelii Chezhegov, Ruslan Nazikov, Aleksandr Beznosikov, Alexander Gasnikov, Lecture Notes in Computer Science, 14766, Mathematical Optimization Theory and Operations Research, 2024, 69
V. S. Amaral, J. O. Lopes, P. S. M. Santos, G. N. Silva, “On the complexity of a quadratic regularization algorithm for minimizing nonsmooth and nonconvex functions”, Optimization Methods and Software, 2024, 1
Anton Klimza, Alexander Gasnikov, Fedor Stonyakin, Mohammad Alkousa, “Universal methods for variational inequalities: Deterministic and stochastic cases”, Chaos, Solitons & Fractals, 187 (2024), 115418
Eduard Gorbunov, Marina Danilova, Innokentiy Shibaev, Pavel Dvurechensky, Alexander Gasnikov, “High-Probability Complexity Bounds for Non-smooth Stochastic Convex Optimization with Heavy-Tailed Noise”, J Optim Theory Appl, 2024
S. S. Ablaev, A. N. Beznosikov, A. V. Gasnikov, D. M. Dvinskikh, A. V. Lobanov, S. M. Puchinin, F. S. Stonyakin, “On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:4 (2024), 587
M. S. Alkousa, A. V. Gasnikov, E. L. Gladin, I. A. Kuruzov, D. A. Pasechnyuk, F. S. Stonyakin, “Solving strongly convex-concave composite saddle-point problems with low dimension of one group of variable”, Sb. Math., 214:3 (2023), 285–333
Evgeniya V. Gasnikova, Aleksandr V. Gasnikov, Demyan V. Yarmoshik, Meruza B. Kubentaeva, Mikhail I. Persiyanov, Irina V. Podlipnova, Ekaterina V. Kotlyarova, Ilya A. Sklonin, Elena D. Podobnaya, Vladislav V. Matyukhin, “O mnogostadiinoi transportnoi modeli i dostatochnykh usloviyakh ee potentsialnosti”, MTIP, 15:2 (2023), 3–17
N. A. Iltyakov, M. A. Obozov, I. M. Dyshlevski, D. V. Yarmoshik, M. B. Kubentaeva, A. V. Gasnikov, E. V. Gasnikova, “On Accelerated Coordinate Descent Methods for Searching Equilibria in Two-Stage Transportation Equilibrium Traffic Flow Distribution Model”, Programmirovanie, 2023, no. 6, 36
Pavel Dvurechensky, Alexander Gasnikov, Alexander Tyurin, Vladimir Zholobov, Springer Proceedings in Mathematics & Statistics, 425, Foundations of Modern Statistics, 2023, 511
T. A. Zvonareva, S. I. Kabanikhin, O. I. Krivorot'ko, “Numerical algorithm for source determination in a diffusion–logistic model from integral data based on tensor optimization”, Comput. Math. Math. Phys., 63:9 (2023), 1654–1663
Nikita Kornilov, Alexander Gasnikov, Pavel Dvurechensky, Darina Dvinskikh, “Gradient-free methods for non-smooth convex stochastic optimization with heavy-tailed noise on convex compact”, Comput Manag Sci, 20:1 (2023)
Artem Vasin, Alexander Gasnikov, Pavel Dvurechensky, Vladimir Spokoiny, “Accelerated gradient methods with absolute and relative noise in the gradient”, Optimization Methods and Software, 38:6 (2023), 1180
N. A. Il'tyakov, M. A. Obozov, I. M. Dyshlevski, D. V. Yarmoshik, M. B. Kubentaeva, A. V. Gasnikov, E. V. Gasnikova, “On Accelerated Coordinate Descent Methods for Searching Equilibria in Two-Stage Transportation Equilibrium Traffic Flow Distribution Model”, Program Comput Soft, 49:6 (2023), 513
Adrien Taylor, Yoel Drori, “An optimal gradient method for smooth strongly convex minimization”, Math. Program., 199:1-2 (2023), 557
E. V. Gasnikova, A. V. Gasnikov, D. V. Yarmoshik, M. B. Kubentaeva, M. I. Persianov, I. V. Podlipnova, E. V. Kotlyarova, I. A. Sklonin, E. D. Podobnaya, V. V. Matyukhin, “Multistage Transportation Model and Sufficient Conditions for Its Potentiality”, Dokl. Math., 108:S1 (2023), S139

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