Journal of Nonlinear Functional Analysis

Abstract

In this paper, some relationships between the second-order contingent derivative and the second-order contingent epiderivative are obtained. By virtute of the second-order contingent derivative of single-valued map with a cone has a compact base, we establish some necessary and sufficient optimality conditions of order 2  for weakly efficient, Henig efficient,  globally efficient and superefficient solutions to the vector equilibrium problem without constraints. Besides, we also investigate the second-order optimality conditions to the vector equilibrium problem with constraints by using the Frechet differentiable functions whose Frechet derivatives are locally Lipschitz.