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

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 func...

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Bibliographic Details
Published in:4OR 2018-06, Vol.16 (2), p.173-198
Main Author: Su, Tran Van
Format: Article
Language:English
Subjects:
Banach spaces
Business and Management
Convexity
Derivatives
Economic models
Equilibrium
Graphs
Industrial and Production Engineering
Neighborhoods
Nonlinear programming
Operations research
Operations Research/Decision Theory
Optimization
Research Paper
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Summary: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.
ISSN:1619-4500
1614-2411
DOI:10.1007/s10288-017-0360-4