Optimal control and approximation for elliptic bilateral obstacle problems
type: Item
instance of: scholarly article
title: Optimal control and approximation for elliptic bilateral obstacle problems
zbMATH Open document ID: 1494.47099
author: Jinjie Liu
author: Xinmin Yang
author: Sheng-Da Zeng
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2021-08-16T00:00:00Z
review text: This paper studies a nonlinear elliptic bilateral obstacle system with a multivalued term given by Clarke's generalized gradient. The existence and uniqueness of weak solution to this problem is obtained, through its formulation as a variational-hemivariational inequality. In addition, a corresponding nonlinear optimal control problem governed by the elliptic system is considered, in which the control variable is the bilateral obstacle, and the existence of an optimal solution is obtained. Then, employing the regularization technique and penalty method, it has been proved that any sequence of solutions to a family of approximating optimal control problems converges to an optimal solution of the original problem.
reviewed by: Mohammad Safdari
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 58E35
Mathematics Subject Classification ID: 35J66
zbMATH DE Number: 7382129
zbMATH Keywords: bilateral obstacle problem
zbMATH Keywords: optimal control
zbMATH Keywords: Clarke's generalized gradient
zbMATH Keywords: existence
zbMATH Keywords: nonhomogeneity
zbMATH Keywords: regularization
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.cnsns.2021.105938
OpenAlex ID: W3174859290
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DOI: 10.1016/J.CNSNS.2021.105938
description: scientific article; zbMATH DE number 7382129