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Strict Feasibility Conditions in Nonlinear Complementarity Problems

Author

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  • Y. B. Zhao

    (Chinese University of Hong Kong
    Chinese Academy of Sciences)

  • D. Li

    (Chinese University of Hong Kong)

Abstract

Strict feasibility plays an important role in the development of the theoryand algorithms of complementarity problems. In this paper, we establishsufficient conditions to ensure strict feasibility of a nonlinearcomplementarity problem. Our analysis method, based on a newly introducedconcept of μ-exceptional sequence, can be viewed as a unified approachfor proving the existence of a strictly feasible point. Some equivalentconditions of strict feasibility are also developed for certaincomplementarity problems. In particular, we show that aP*-complementarity problem is strictly feasible if and only ifits solution set is nonempty and bounded.

Suggested Citation

  • Y. B. Zhao & D. Li, 2000. "Strict Feasibility Conditions in Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 641-664, December.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:3:d:10.1023_a:1026459501988
    DOI: 10.1023/A:1026459501988
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    References listed on IDEAS

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    1. Masakazu Kojima & Nimrod Megiddo & Toshihito Noma, 1991. "Homotopy Continuation Methods for Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 16(4), pages 754-774, November.
    2. G. Isac & W. T. Obuchowska, 1998. "Functions Without Exceptional Family of Elements and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 147-163, October.
    3. Francisco Facchinei, 1998. "Structural and Stability Properties of P 0 Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 735-745, August.
    4. Y. B. Zhao & G. Isac, 2000. "Quasi-P*-Maps, P(τ, α, β)-Maps, Exceptional Family of Elements, and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 213-231, April.
    5. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. G. Isac & S. Z. Németh, 2006. "Duality of Implicit Complementarity Problems by Using Inversions and Scalar Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 621-633, March.
    2. J. H. Fan & X. G. Wang, 2009. "Solvability of Generalized Variational Inequality Problems for Unbounded Sets in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 59-74, October.
    3. Yun-Bin Zhao & Duan Li, 2001. "On a New Homotopy Continuation Trajectory for Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 119-146, February.

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