New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces

Tran Van Su ()
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Tran Van Su: Quangnam University

4OR, 2018, vol. 16, issue 2, No 3, 173-198

Abstract: Abstract This article presents necessary and sufficient optimality conditions for weakly efficient solution, Henig efficient solution, globally efficient solution and superefficient solution of vector equilibrium problem without constraints in terms of contingent derivatives in Banach spaces with stable functions. Using the steadiness and stability on a neighborhood of optimal point, necessary optimality conditions for efficient solutions are derived. Under suitable assumptions on generalized convexity, sufficient optimality conditions are established. Without assumptions on generalized convexity, a necessary and sufficient optimality condition for efficient solutions of unconstrained vector equilibrium problem is also given. Many examples to illustrate for the obtained results in the paper are derived as well.

Keywords: Optimality conditions; Unconstrained vector equilibrium problem; Contingent derivatives; Steady functions; Stable functions; Weakly efficient solutions; Henig efficient solutions; Globally efficient solutions; Superefficient solutions; 90C46; 91B50; 90C29; 90C48; 49J52 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10288-017-0360-4

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