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Theorems of the Alternative and Optimization with Set-Valued Maps
Authors:X M Yang  X Q Yang  G Y Chen
Institution:(1) Department of Mathematics, Chongqing Normal University, Chongqing, China;(2) Present address: Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;(3) Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;(4) Institute of Systems Science, Chinese Academy of Sciences, Beijing, China
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.
Keywords:vector optimization  set-valued maps  generalized convexity  equivalent conditions  theorem of the alternatives  optimality conditions
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