Second-Order Necessary and Sufficient Efficiency Conditions for Nonsmooth Semi-Infinite Multiobjective Optimization Problems

We present second-order necessary and sufficient conditions for weak efficiency of nonsmooth semi-infinite multiobjective programming involving inequality, equality and set constraints in terms of the Páles-Zeidan second-order directional derivatives. Sufficient optimality conditions are established in two cases. They include the case without assumptions on generalized convexity and the case with assumptions on the 2-generalized convexity together with second-order duality theorems of Mond-Weir type.