Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications
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Fritz John and Karush–Kuhn–Tucker necessary conditions for local efficient solutions of constrained vector equilibrium problems in Banach spaces in which those solutions are regular in the sense of Ioffe via convexificators are established. Under suitable assumptions on generalized convexity, sufficient conditions are derived. Some applications to constrained vector variational inequalities and constrained vector optimization problems are also given.
KeywordsVector equilibrium problems Vector variational inequalities Vector optimization problems Regular points in the sense of Ioffe Fritz John and Karush–Kuhn–Tucker optimality conditions Convexificators
Mathematics Subject Classification90C46 91B50 49J52
The author is grateful to the referees for their valuable comments and suggestions which improve the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2014.61.
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