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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.
DOI:
https://doi.org/10.7868/S0044466915020064
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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
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http://mi.mathnet.ru/eng/zvmmf10152 http://mi.mathnet.ru/eng/zvmmf/v55/i2/p213
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This publication is cited in the following articles:
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Andrei V. Chernov, “O suschestvovanii ravnovesiya po Neshu v differentsialnoi igre, svyazannoi s ellipticheskimi uravneniyami: monotonnyi sluchai”, MTIP, 7:3 (2015), 48–78
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