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Theorems of the Alternative and Optimization with Set-Valued Maps

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Abstract

In this paper, the concept of generalized cone subconvexlike set-valued mapsis presented and a theorem of alternative for the system of generalizedinequality–equality set-valued maps is established. By applying thetheorem of the alternative and other results, necessary and sufficientoptimality conditions for vector optimization problems with generalizedcone subconvexlike set-valued maps are obtained.

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Yang, X.M., Yang, X.Q. & Chen, G.Y. Theorems of the Alternative and Optimization with Set-Valued Maps. Journal of Optimization Theory and Applications 107, 627–640 (2000). https://doi.org/10.1023/A:1026407517917

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  • DOI: https://doi.org/10.1023/A:1026407517917

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