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This article is cited in 7 scientific papers (total in 7 papers)
Optimization, System Analysis, and Operations Research
Accelerated gradient-free optimization methods with a non-Euclidean proximal operator
E. Vorontsovaab, A. V. Gasnikovcde, E. A. Gorbunovc, P. E. Dvurechenskiif a Far Eastern Federal University, Vladivostok, Russia
b Université Grenoble Alpes, Grenoble, France
c Moscow Institute of Physics and Technology, Moscow, Russia
d National Research University Higher School of Economics, Moscow, Russia
e Caucasus Mathematical Center, Adyghe State University, Maikop, Republic of Adygea, Russia
f Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Abstract:
We propose an accelerated gradient-free method with a non-Euclidean proximal operator associated with the $p$-norm ($1\leqslant p\leqslant 2$). We obtain estimates for the rate of convergence of the method under low noise arising in the calculation of the function value. We present the results of computational experiments.
Keywords:
accelerated optimization methods, convex optimization, non-gradient methods, inaccurate oracle, non-Euclidean proximal operator, prox-structure.
Received: 21.04.2018 Revised: 05.11.2018 Accepted: 08.11.2018
Citation:
E. Vorontsova, A. V. Gasnikov, E. A. Gorbunov, P. E. Dvurechenskii, “Accelerated gradient-free optimization methods with a non-Euclidean proximal operator”, Avtomat. i Telemekh., 2019, no. 8, 149–168; Autom. Remote Control, 80:8 (2019), 1487–1501
Linking options:
https://www.mathnet.ru/eng/at15320 https://www.mathnet.ru/eng/at/y2019/i8/p149
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Abstract page: | 325 | Full-text PDF : | 59 | References: | 53 | First page: | 26 |
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