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

Do Van Luu; Nguyen Lam Tung

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

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

Mathematics Subject Classification

90C46, 90C29

Suggested citation

D. V. Luu, N. L. Tung. “Second-Order Necessary and Sufficient Efficiency Conditions for Nonsmooth Semi-Infinite Multiobjective Optimization Problems.” Journal of Convex Analysis 31 (2024), No. 4, 1189–1202.