## Tran Van Su, Second-order efficiency conditions for \$C^{1,1}\$-vector equilibrium problems in terms of contingent derivatives and applications

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DOI: 10.23952/jnva.3.2019.3.07
Volume 3, Issue 3, 1 December 2019, Pages 317-332

Abstract. 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.

Tran Van Su, Second-order efficiency conditions for $C^{1,1}$-vector equilibrium problems in terms of contingent derivatives and applications, J. Nonlinear Var. Anal. 3 (2019), 317-332.