Abstract
We propose an accelerated gradient-free method with a non-Euclidean proximal operator associated with the p-norm (1 ⩽ p ⩽ 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.
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Acknowledgments
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.
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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 8, pp. 149–168.
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Vorontsova, E.A., Gasnikov, A.V., Gorbunov, E.A. et al. Accelerated Gradient-Free Optimization Methods with a Non-Euclidean Proximal Operator. Autom Remote Control 80, 1487–1501 (2019). https://doi.org/10.1134/S0005117919080095
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DOI: https://doi.org/10.1134/S0005117919080095