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On Nondifferentiable and Nonconvex Vector Optimization Problems

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University)

  • J> C> Yao

    (National Sun Yat-sen University)

Abstract

In this paper, we prove the equivalence among the Minty vector variational-like inequality, Stampacchia vector variational-like inequality, and a nondifferentiable and nonconvex vector optimization problem. By using a fixed-point theorem, we establish also an existence theorem for generalized weakly efficient solutions to the vector optimization problem for nondifferentiable and nonconvex functions.

Suggested Citation

  • Q. H. Ansari & J> C> Yao, 2000. "On Nondifferentiable and Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 475-488, September.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:3:d:10.1023_a:1004697127040
    DOI: 10.1023/A:1004697127040
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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.
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    Cited by:

    1. 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.
    2. T. Jabarootian & J. Zafarani, 2008. "Generalized Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 15-30, January.
    3. S. Al-Homidan & Q. H. Ansari & S. Schaible, 2007. "Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 515-531, September.
    4. Q. H. Ansari & G. M. Lee, 2010. "Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 1-16, April.
    5. S. K. Mishra & S. Y. Wang & K. K. Lai, 2008. "Gap Function for Set-Valued Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 77-84, July.
    6. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, January.

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