Characterizing the Solution Set for Nonconvex Semi-Infinite Programs Involving Tangential Subdifferentials
Xian-Jun Long, Juan Liu, Nan‐jing Huang
Abstract
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.
Topics & Concepts
MathematicsLagrange multiplierSemi-infinite programmingSet (abstract data type)Solution setMathematical optimizationLagrangianFunction (biology)Applied mathematicsConstant functionMathematical analysisRegular polygonPiecewiseGeometryComputer scienceBiologyProgramming languageEvolutionary biologyOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchContact Mechanics and Variational Inequalities