New Second-Order Optimality Conditions for Vector Equilibrium Problems with Constraints in Terms of Contingent Derivatives

摘要

In this paper, we establish the primal and dual second-order necessary and sufficient optimality conditions for (local) weakly efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives with 2-steady functions in real finite spaces. Using the 2-steadiness of objective and constraint functions at a given optimal point, the second-order necessary conditions for weakly efficient solutions of constrained vector equilibrium problems are derived. Under the suitable assumptions on 2-steadiness of objective and constraint functions, the dual second-order necessary optimality conditions will become the dual second-order sufficient optimality conditions. We also give several examples that illustrate our results.