A Relaxation Approach to Discretization of Boundary Optimal Control Problems of Semilinear Parabolic Equations
Year: 2019
Author: B. Kokkinis
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 5 : pp. 731–744
Abstract
We consider an optimal boundary control problem described by a semilinear parabolic partial differential equation, with control and state constraints. Since this problem may have no classical solutions, it is reformulated in the relaxed form. The relaxed control problem is discretized by using a finite element method in space and a partially implicit scheme in time, while the controls are approximated by piecewise constant relaxed controls. We first state the necessary conditions for optimality for the continuous problem and the discrete relaxed problem. Next, under appropriate assumptions, we prove that accumulation points of sequences of optimal (resp. admissible and extremal) discrete relaxed controls are optimal (resp. admissible and extremal) for the continuous relaxed problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-13251
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 5 : pp. 731–744
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Boundary optimal control semilinear parabolic systems state constraints relaxed controls discretization.