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Gradient-free proximal methods with inexact oracle for convex stochastic nonsmooth optimization problems on the simplex

  • Stochastic Systems, Queueing Systems
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Abstract

In this paper we propose a modification of the mirror descent method for non-smooth stochastic convex optimization problems on the unit simplex. The optimization problems considered differ from the classical ones by availability of function values realizations. Our purpose is to derive the convergence rate of the method proposed and to determine the level of noise that does not significantly affect the convergence rate.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    A. V. Gasnikov, A. A. Lagunovskaya, I. N. Usmanova & F. A. Fedorenko

  2. Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia

    A. V. Gasnikov & I. N. Usmanova

  3. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    A. A. Lagunovskaya

Authors
  1. A. V. Gasnikov
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  2. A. A. Lagunovskaya
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  3. I. N. Usmanova
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  4. F. A. Fedorenko
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Correspondence to A. V. Gasnikov.

Additional information

Original Russian Text © A.V. Gasnikov, A.A. Lagunovskaya, I.N. Usmanova, F.A. Fedorenko, 2016, published in Avtomatika i Telemekhanika, 2016, No. 10, pp. 57–77.

This paper was recommended for publication by P.S. Shcherbakov, a member of the Editorial Board

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Gasnikov, A.V., Lagunovskaya, A.A., Usmanova, I.N. et al. Gradient-free proximal methods with inexact oracle for convex stochastic nonsmooth optimization problems on the simplex. Autom Remote Control 77, 2018–2034 (2016). https://doi.org/10.1134/S0005117916110114

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  • DOI: https://doi.org/10.1134/S0005117916110114

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