Journal of Convex Analysis 31 (2024), No. 4, 1189--1202
Copyright Heldermann Verlag 2024
Second-Order Necessary and Sufficient Efficiency Conditions for Nonsmooth Semi-Infinite Multiobjective Optimization Problems
Do Van Luu
Institute of Mathematics and Applied Sciences, Thang Long University, Hanoi, Vietnam
dvluu@math.ac.vn
Nguyen Lam Tung
Mathematics Department, Thang Long University, Hanoi, Vietnam
nguyenlamtung01@gmail.com
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.
Keywords: Second-order necessary efficiency conditions, Pales-Zeidan second-order directional derivatives, first and second-order tangent vectors, second-order constraint qualifications, nonsmooth semi-infinite multiobjective optimization problem.
MSC: 90C46, 90C29.
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