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Optimal Control of Elliptic Variational–Hemivariational Inequalities

Author

Listed:
  • Zijia Peng

    (Guangxi University for Nationalities)

  • Karl Kunisch

    (Karl-Franzens-Universität Graz)

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.

Suggested Citation

  • Zijia Peng & Karl Kunisch, 2018. "Optimal Control of Elliptic Variational–Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 1-25, July.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:1:d:10.1007_s10957-018-1303-8
    DOI: 10.1007/s10957-018-1303-8
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    References listed on IDEAS

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    1. Leszek Gasiński & Zhenhai Liu & Stanisław Migórski & Anna Ochal & Zijia Peng, 2015. "Hemivariational Inequality Approach to Evolutionary Constrained Problems on Star-Shaped Sets," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 514-533, February.
    2. A. Lahmdani & O. Chadli & J. C. Yao, 2014. "Existence of Solutions for Noncoercive Hemivariational Inequalities by an Equilibrium Approach Under Pseudomonotone Perturbation," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 49-66, January.
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    Cited by:

    1. Shih-Sen Chang & Salahuddin & Lin Wang & Jinfang Tang & Liangcai Zhao, 2022. "Optimal Control Problems for Set-Valued Quasivariational Inequalities with Applications," Mathematics, MDPI, vol. 10(5), pages 1-19, February.

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