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Vector Variational Inequalities and the (S)+ Condition

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  • Y. Chiang

    (National Sun Yat-Sen University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

Let $${\cal Z}$$ and X be Hausdorff real topological vector spaces and let $${\cal L}_b(X,{\cal Z})$$ be the space of continuous linear mappings from X into $${\cal Z}$$ equipped with the topology of bounded convergence. In this paper, we define the (S)+ condition for operators from a nonempty subset of X into $${\cal L}_b(X,{\cal Z})$$ and derive some existence results for vector variational inequalities with operators of the class (S)+. Some applications to vector complementarity problems are given.

Suggested Citation

  • Y. Chiang & J. C. Yao, 2004. "Vector Variational Inequalities and the (S)+ Condition," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 271-290, November.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:2:d:10.1007_s10957-004-5149-x
    DOI: 10.1007/s10957-004-5149-x
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    References listed on IDEAS

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    1. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    2. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
    3. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
    4. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
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    Cited by:

    1. Júlia Salamon, 2010. "Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems," Journal of Global Optimization, Springer, vol. 47(2), pages 173-183, June.
    2. Y. Chiang, 2005. "The (S) + 1 Condition for Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 581-594, March.

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