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Duality of Implicit Complementarity Problems by Using Inversions and Scalar Derivatives

Author

Listed:
  • G. Isac

    (Royal Military College of Canada)

  • S. Z. Németh

    (Hungarian Academy of Sciences)

Abstract

The notion of infinitesimal exceptional family of elements for an ordered pair of mappings is introduced. By using a special inversion mapping, a duality between the exceptional family of elements for an ordered pair of mappings and the infinitesimal exceptional family of elements for an ordered pair of mappings is presented. By using this duality and the notion of scalar derivatives, existence theorems for implicit complementarity problems in Hilbert spaces are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:3:d:10.1007_s10957-006-9035-6
    DOI: 10.1007/s10957-006-9035-6
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    References listed on IDEAS

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    1. 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.
    2. Vyacheslav Kalashnikov & George Isac, 2002. "Solvability of Implicit Complementarity Problems," Annals of Operations Research, Springer, vol. 116(1), pages 199-221, October.
    3. 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.
    4. Y. B. Zhao & J. Y. Han & H. D. Qi, 1999. "Exceptional Families and Existence Theorems for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 475-495, May.
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