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Existence of Solutions to Implicit Vector Variational Inequalities

Author

Listed:
  • Y. Chiang

    (National Sun Yat-Sen University)

  • O. Chadli

    (University Ibn Zohr)

  • J.C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, we study a class of implicit vector variational inequalities which contain implicit variational inequalities and generalized quasivariational inequalities as special cases. By employing the Fan–Kakutani fixed-point theorem and the Oettli scalarization procedure, respectively, we establish several existence results for implicit vector variational inequalities.

Suggested Citation

  • Y. Chiang & O. Chadli & J.C. Yao, 2003. "Existence of Solutions to Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 251-264, February.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:2:d:10.1023_a:1022472103162
    DOI: 10.1023/A:1022472103162
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    References listed on IDEAS

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    1. Jun-Yi Fu, 2000. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 57-64, September.
    2. Jen-Chih Yao, 1995. "Generalized-Quasi-Variational Inequality Problems with Discontinuous Mappings," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 465-478, May.
    3. O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
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    Cited by:

    1. Jian-Wen Peng & Soon-Yi Wu & Yan Wang, 2012. "Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints," Journal of Global Optimization, Springer, vol. 52(4), pages 779-795, April.

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