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Avtomatika i Telemekhanika, 2019, Issue 8, Pages 149–168
DOI: https://doi.org/10.1134/S0005231019080117 (Mi at15320) 		 
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
Full-text PDF (854 kB) Citations (7)
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DOI: https://doi.org/10.1134/S0005231019080117
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.
Funding agency Grant number
Russian Science Foundation 17-11-01027
Ministry of Education and Science of the Russian Federation
МД-1320.2018.1
Russian Foundation for Basic Research 18-31-20005_мол_а_вед
18-29-03071_мк
The work shown in Section 3 was supported by the Russian Science Foundation, project no. 17-11-01027. In the remaining sections, the work of A.V. Gasnikov was funded within the framework of the State Support of the Leading Universities of the Russian Federation “5-100” and was supported by the Russian Foundation for Basic Research, project no. 18-31-20005 mol-a-ved, the work of E.A. Gorbunov was supported by the grant of the President of the Russian Federation MD-1320.2018.1, the work of P.E. Dvurechenskii and E.A. Vorontsova was supported by the Russian Foundation for Basic Research, project no. 18-29-03071 mk.

Received: 21.04.2018
Revised: 05.11.2018
Accepted: 08.11.2018
English version:
Automation and Remote Control, 2019, Volume 80, Issue 8, Pages 1487–1501
DOI: https://doi.org/10.1134/S0005117919080095
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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\paper Accelerated gradient-free optimization methods with a non-Euclidean proximal operator
\jour Avtomat. i Telemekh.
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\issue 8
\pages 149--168
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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