Theorems of the Alternative and Optimization with Set-Valued Maps

X. M. Yang, X. Q. Yang and G. Y. Chen
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X. M. Yang: Chongqing Normal University
X. Q. Yang: Hong Kong Polytechnic University, Hung Hom
G. Y. Chen: Chinese Academy of Sciences

Journal of Optimization Theory and Applications, 2000, vol. 107, issue 3, No 12, 627-640

Abstract: 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 (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (9)

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DOI: 10.1023/A:1026407517917

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