OPTIMALITY CONDITIONS FOR WEAKLY EFFICIENT SOLUTION OF VECTOR EQUILIBRIUM PROBLEM WITH CONSTRAINTS IN TERMS OF SECOND-ORDER CONTINGENT DERIVATIVES

Abstract

In this paper, we present second-order necessary and sufficient optimality conditions for weakly efficient solution of a vector equilibrium problem with constraints (in short, VEPC ) in terms of second-order contingent derivative and second-order asymptotic contingent derivative. With this purpose, we impose the objective functions, either all them are twice Fr\'echet differentiable at optimal point or the Fr\'echet derivatives are calm at optimal point or the profile mappings has the cone-Aubin properties. Besides, we also can invoke constraint qualifications of the Kurcyusz - Robinson - Zowe (KRZ) type. Our paper point out new improvements from the known results of Gutierrez, Jim\'enez and Novo (2010) and Khanh and Tung (2015); see [8], [10] in cases of single valued optimization and give some discusses about it.