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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 2, Pages 213–228
DOI: https://doi.org/10.7868/S0044466915020064 (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
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DOI: https://doi.org/10.7868/S0044466915020064
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
Received: 27.05.2014
Revised: 06.07.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 2, Pages 212–226
DOI: https://doi.org/10.1134/S0965542515020062
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
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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