Variational Principles for Vector Equilibrium Problems Related to Conjugate Duality

Abstract: This paper deals with the characterization of solutions for vector equilibrium problems by means of conjugate duality. By using the Fenchel duality we establish variational principles, that is, optimization problems with set-valued objective functions, the solution sets of which contain the ones of the vector equilibrium problems. The set-valued objective mappings depend on the data, but not on the solution sets of the vector equilibrium problems. As a particular instance we obtain gap functions for the weak vector variational inequality problem.

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