An Approximating Approach to an Optimal Control Problem for an Elliptic Variational Inequality on a Mixed Boundary⋆. (4th July 2022)

• Record Type: Journal Article
• Authors: Duan, Yarui; Wu, Pengcheng; Zhou, Yuying
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 9(2022)
• Page Start: 1095
• Page End: 1113
• Publication Date: 2022-07-04
• Subjects: Double obstacle elliptic variational inequality -- mixed boundary optimal control problem -- penalty approximation method -- the necessary optimality conditions; 49J20 -- 49K20 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2086570
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, an optimal control problem (OCP) for a system governed by a class of double obstacle elliptic variational inequalities on a mixed boundary is proposed. An approximating optimal control problem ( OCP ) ε is then defined to approximate the original problem (OCP) by a penalty method. Under some assumptions, the existence result for the problem ( OCP ) ε is proved. The sequence of solutions to the problem ( OCP ) ε converges to a solution of the original problem (OCP) as the penalty parameter tends to zero. Next, the necessary optimality conditions are obtained for the solution of the problem ( OCP ) ε with a given concrete penalty function. At last, an algorithm is used to solve a given concrete optimal control problem. Numerical experimental results are presented to show that the approximation method is effective and practical.