Second-order efficiency conditions for $C^{1,1}$-vector equilibrium problems in terms of contingent derivatives and applications
Journal of Nonlinear and Variational Analysis · 2019
In this paper, we study the Fritz John and Kuhn-Tucker second-order necessary and sufficient optimality conditions for C 1,1 -vector equilibrium problems in terms of contingent derivatives.By applying the strong separation theorem of disjoint convex sets in convex analysis, we establish the Fritz John necessary optimality conditions for a local weakly efficient solution of VEPC.We also propose the Kurcyusz-Robinson-Zowe constraint qualification in order to obtain the Kuhn-Tucker necessary optimality conditions.By making use of both the second-order contingent derivatives and the second-order asymptotic contingent derivatives for the class of locally Lipschitz functions in which its derivatives are locally Lipschitz, we obtain a second-order sufficient optimality condition for the problem considered above.As an application, we derive Fritz John and Kuhn-Tucker second-order necessary and sufficient optimality conditions for constrained vector variational inequalities and constrained vector optimization problems.