Second-Order Efficiency Conditions for Vector Equilibrium Problems with Constraints via Contingent Epiderivatives

We establish second-order necessary and sufficient conditions for weakly efficient, Henig efficient, globally efficient and superefficient solutions of vector equilibrium problems with constraints in terms of contingent epiderivatives in Banach spaces. Firstly, some results on the existence and the uniqueness of second-order contingent epiderivatives with the functions defined on infinite-dimensional spaces are established. Secondly, under suitable assumptions, second-order necessary and sufficient conditions for weakly efficient solutions of such problems are derived. As applications, we provide the second-order necessary and sufficient efficiency conditions for Henig efficient, globally efficient and superefficient solutions of constrained vector equilibrium problems via contingent epiderivatives. Some illustrative examples are given as well.