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A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces

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  • Zhi-Ang Zhou
  • Jian-Wen Peng

Abstract

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimization problems were established in the sense of globally proper efficiency.

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  • Zhi-Ang Zhou & Jian-Wen Peng, 2012. "A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, October.
    • Handle: RePEc:hin:jnljam:370654
    DOI: 10.1155/2012/370654
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    Cited by:

    1. Renying Zeng, 2023. "On Sub Convexlike Optimization Problems," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

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