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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 2, Pages 213–228 (Mi zvmmf10152)  

This article is cited in 1 scientific paper (total in 1 paper)

On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation

A. V. Chernovab

a Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia
b Nizhni Novgorod State Technical University, ul. Minina 24, Nizhni Novgorod, 603950, Russia

Abstract: The optimal control of a second-order semilinear elliptic diffusion-reaction equation is considered. Sufficient conditions for the convergence of the conditional gradient method are obtained without using assumptions (traditional for optimization theory) that ensure the Lipschitz continuity of the objective functional derivative. The total (over the entire set of admissible controls) preservation of solvability, a pointwise estimate of solutions, and the uniqueness of a solution to the homogeneous Dirichlet problem for a controlled elliptic equation are proved as preliminary results, which are of interest on their own.

Key words: semilinear elliptic diffusion-reaction equations, conditional gradient method, total preservation of solvability, solution estimate, solution uniqueness.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.В.49.21.0003
1727


DOI: https://doi.org/10.7868/S0044466915020064

Full text: PDF file (322 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:2, 212–226

Bibliographic databases:

UDC: 519.626
Received: 27.05.2014
Revised: 06.07.2014

Citation: A. V. Chernov, “On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:2 (2015), 213–228; Comput. Math. Math. Phys., 55:2 (2015), 212–226

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Andrei V. Chernov, “O suschestvovanii ravnovesiya po Neshu v differentsialnoi igre, svyazannoi s ellipticheskimi uravneniyami: monotonnyi sluchai”, MTIP, 7:3 (2015), 48–78  mathnet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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