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Solvability of Implicit Complementarity Problems

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  • Vyacheslav Kalashnikov
  • George Isac

Abstract

In this paper, a new notion of exceptional family of elements (EFE) for a pair of functions involved in the implicit complementarity problem (ICP) is introduced. Based upon this notion and the Leray–Schauder Alternative, a general alternative is obtained which gives more general existence theorems for the implicit complementarity problem. Finally, via the techniques of continuous selections, these existence theorems are extended to the multi-valued implicit complementarity problems (MIPS). Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Vyacheslav Kalashnikov & George Isac, 2002. "Solvability of Implicit Complementarity Problems," Annals of Operations Research, Springer, vol. 116(1), pages 199-221, October.
    • Handle: RePEc:spr:annopr:v:116:y:2002:i:1:p:199-221:10.1023/a:1021388515849
    DOI: 10.1023/A:1021388515849
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    Cited by:

    1. Meng-Meng Zheng & Zheng-Hai Huang & Xiao-Xiao Ma, 2020. "Nonemptiness and Compactness of Solution Sets to Generalized Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 80-98, April.
    2. 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.
    3. Tong-tong Shang & Jing Yang & Guo-ji Tang, 2022. "Generalized Polynomial Complementarity Problems over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 443-483, February.

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