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Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations

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  • Yi-bin Xiao

    (University of Electronic Science and Technology of China)

  • Nan-jing Huang

    (Sichuan University)

Abstract

In this paper, we consider an extension of well-posedness for a minimization problem to a class of variational–hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed variational–hemivariational inequality and give some conditions under which the variational–hemivariational inequality is strongly well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational–hemivariational inequality and the well-posedness of corresponding inclusion problem.

Suggested Citation

  • Yi-bin Xiao & Nan-jing Huang, 2011. "Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 33-51, October.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:1:d:10.1007_s10957-011-9872-9
    DOI: 10.1007/s10957-011-9872-9
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    References listed on IDEAS

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    1. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.
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    7. M. Margiocco & F. Patrone & L. Pusillo, 2002. "On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 361-379, February.
    8. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
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