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REFE-Acceptable Mappings: Necessary and Sufficient Condition for the Nonexistence of a Regular Exceptional Family of Elements

Author

Listed:
  • G. Isac

    (Royal Military College of Canada)

  • S. Z. Németh

    (University of Birmingham)

Abstract

By considering the notion of regular exceptional family of elements (REFE), we define the class of REFE-acceptable mappings. By definition, a complementarity problem on a Hilbert space defined by a REFE-acceptable mapping and a closed convex cone has either a solution or a REFE. We present several classes of REFE-acceptable mappings. For this, neither the topological degree nor the Leray-Schauder alternative is necessary. By using the concept of REFE-acceptable mappings, we present necessary and sufficient conditions for the nonexistence of regular exceptional family of elements. These conditions are used for generating several existence theorems and existence and uniqueness theorems for complementarity problems.

Suggested Citation

  • G. Isac & S. Z. Németh, 2008. "REFE-Acceptable Mappings: Necessary and Sufficient Condition for the Nonexistence of a Regular Exceptional Family of Elements," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 507-520, June.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-007-9344-4
    DOI: 10.1007/s10957-007-9344-4
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    References listed on IDEAS

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    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. M. Bianchi & N. Hadjisavvas & S. Schaible, 2004. "Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 1-17, July.
    3. 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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