Characterizing the Solution Set for Nonconvex Semi-Infinite Programs Involving Tangential Subdifferentials
Xian-Jun Long, Juan Liu, Nan‐jing Huang · Numerical Functional Analysis and Optimization · 2021
The purpose of this paper is to study the characterization of the solution set for nonconvex semi-infinite programming problems related to tangential subdifferentials. We give a necessary optimality condition for the solution set of the nonconvex semi-infinite programming problem. We also prove that the Lagrangian function associated with a fixed Lagrange multiplier is constant on the solution set for semi-infinite programming problems. Finally, by using Dini pseudoconvexity, we obtain two characterizations of the solution set of the problem considered in this paper. Some examples are given to illustrate our results.