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On the Equivalence of Extended Generalized Complementarity and Generalized Least-Element Problems

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University
    National Sun Yat-sen University)

  • T. C. Lai

    (National Taiwan University)

  • J. C. Yao

    (National Sun Yat-sen University)

Abstract

In this paper, we derive some equivalences of generalized nonlinear programs, generalized least-element problems, and extended generalized complementarity problems under certain regularity and growth conditions. We also generalize the notion of a Z-map for point-to-set maps. Our results extend recent results by Schaible and Yao (Ref. 1).

Suggested Citation

  • Q. H. Ansari & T. C. Lai & J. C. Yao, 1999. "On the Equivalence of Extended Generalized Complementarity and Generalized Least-Element Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 277-288, August.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021724306242
    DOI: 10.1023/A:1021724306242
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    References listed on IDEAS

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    1. Romesh Saigal, 1976. "Extension of the Generalized Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 260-266, August.
    2. 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.
    3. R. C. Riddell, 1981. "Equivalence of Nonlinear Complementarity Problems and Least Element Problems in Banach Lattices," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 462-474, August.
    4. Richard W. Cottle & Jong-Shi Pang, 1978. "A Least-Element Theory of Solving Linear Complementarity Problems as Linear Programs," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 155-170, May.
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    Citations

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    Cited by:

    1. E. Allevi & A. Gnudi & S. Schaible & M. Vespucci, 2010. "Equilibrium and least element problems for multivalued functions," Journal of Global Optimization, Springer, vol. 46(4), pages 561-569, April.
    2. Huang, N.J. & Yang, X.Q. & Chan, W.K., 2007. "Vector complementarity problems with a variable ordering relation," European Journal of Operational Research, Elsevier, vol. 176(1), pages 15-26, January.
    3. F. Giannessi & G. Mastroeni & X. Yang, 2012. "Survey on Vector Complementarity Problems," Journal of Global Optimization, Springer, vol. 53(1), pages 53-67, May.
    4. Y.-P. Fang & N.-J. Huang, 2007. "Equivalence of Equilibrium Problems and Least Element Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 411-422, March.

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