Optimal Control of Elliptic Variational–Hemivariational Inequalities

Zijia Peng () and Karl Kunisch ()
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Zijia Peng: Guangxi University for Nationalities
Karl Kunisch: Karl-Franzens-Universität Graz

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 1, No 1, 25 pages

Abstract: Abstract This paper deals with the optimality system of an optimal control problem governed by a nonlinear elliptic inclusion and a nonsmooth cost functional. The system describing the state consists of a variational–hemivariational inequality, the solution mapping of which with respect to the control is proved to be weakly closed. Existence of optimal pairs for the optimal control problem is obtained. Approximation results and abstract necessary optimality conditions of first order are derived based on the adapted penalty method and nonsmooth analysis techniques. Moreover, the optimality system for a class of obstacle problems with nonmonotone perturbation is given.

Keywords: Hemivariational inequality; Optimality system; Necessary optimality condition; Obstacle; 47J20; 49J20; 49J40; 49K20 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1303-8

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