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Existence of Solutions for Generalized Vector Variational-like Inequalities

Author

Listed:
  • L. C. Ceng

    (Shanghai Normal University)

  • S. Schaible

    (University of California)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, we consider a generalized vector variational-like inequality problem (for short, GVVLIP), which includes generalized vector variational inequalities, vector variational inequalities and classical variational inequalities as special cases. The concepts of generalized C-pseudomonotone-like and generalized H-hemicontinuous-like operators are introduced. Some existence results for GVVLIP are obtained under the assumptions of generalized C-pseudomonotone-like property and generalized H-hemicontinuous-like property. These results appear to be new and interesting. New existence results of the classical variational inequality are also obtained.

Suggested Citation

  • L. C. Ceng & S. Schaible & J. C. Yao, 2008. "Existence of Solutions for Generalized Vector Variational-like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 121-133, April.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:1:d:10.1007_s10957-007-9336-4
    DOI: 10.1007/s10957-007-9336-4
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    References listed on IDEAS

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    1. 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.
    2. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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    Cited by:

    1. Xing Wang & Nan-Jing Huang, 2013. "Differential Vector Variational Inequalities in Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 109-129, July.

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