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Numerical Study of High-Dimensional Optimization Problems Using a Modification of Polyak’s Method

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Abstract

A modification of Polyak’s special method of convex optimization is proposed. The properties of the corresponding algorithm are studied by computational experiments for convex separable and nonseparable optimization problems, nonconvex optimization problems for the potentials of atomic-molecular clusters, and a model optimal control problem. Sequential and parallel versions of the algorithm have been implemented, which made it possible to solve problems with dimensions of up to one hundred billion variables.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-07-00587.

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Authors and Affiliations

  1. Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    A. Yu. Gornov & A. S. Anikin

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    A. N. Andrianov

Authors
  1. A. Yu. Gornov
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  2. A. S. Anikin
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  3. A. N. Andrianov
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Corresponding authors

Correspondence to A. Yu. Gornov or A. S. Anikin.

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Translated by E. Chernokozhin

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Gornov, A.Y., Anikin, A.S. & Andrianov, A.N. Numerical Study of High-Dimensional Optimization Problems Using a Modification of Polyak’s Method. Comput. Math. and Math. Phys. 61, 1053–1062 (2021). https://doi.org/10.1134/S0965542521070034

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  • DOI: https://doi.org/10.1134/S0965542521070034

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