The Research On Optimality Conditions And Duality Theory Of Semi-Infinite Programming

Semi-infinite programming is an optimization problem with finite decision variables and infinite constraint functions.In recent years,the semi-infinite programming problem has attracted extensive attention from many scholars at home and abroad.This is because semi-infinite programming has extensive and direct applications in the fields of Chebyshev approximation,robust optimization,minimax problem,design center method,selection programming and so on.At present,the semi-infinite programming problems is mainly studied by Clarke subdifferentials.This requires the assumption that the function is local Lipschitz.In this paper,we study the optimality conditions and duality theory of semi-infinite programming problems without local Lipschitz assumption.The main arrangements are as follows:The first chapter briefly describes the research background and significance of the semi-infinite programming problem,and introduces some basic concepts and preliminary results.In chapter 2,the optimality conditions and solution set characterizations of semi-infinite programming problems are mainly discussed.Firstly,the necessary conditions of the existence of solution set for nonconvex semi-infinite programming problems are established by using constraint specification,and sufficient conditions for the solution of non-convex semi-infinite programming problems are established by using Dini quasiconvexity.Then,using Dini pseudoconvexity,we describe two kinds of equivalent solution sets for tangential subdifferentials of nonconvex semi-infinite programming problems,and illustrate corresponding results with examples.In chapter 3,we mainly discuss the optimality conditions and characterization of robust optimal solution set for nonconvex semi-infinite programming with uncertain parameters in objectives and constraint functions.Firstly,the uncertain semi-infinite programming problem is transformed into its robust equivalence problem,i.e.min-max robust optimization problem.Then,using robust constraints,the necessary and sufficient conditions for robust optimal solution of nonconvex uncertain semi-infinite programming problem are established by robust optimization method.Finally,using Dini pseudoconvex functions,the equivalence characterization of robust optimal solution set for nonconvex uncertain semi-infinite programming problems is given.In chapter 4,the optimality conditions and duality theory of approximate solutions for multiobjective semi-infinite programming problems are mainly discussed.Firstly,the necessary conditions for weakly quasi ?-efficient solutions of nonconvex multiobjective semi-infinite programming problems are established by using the constraint specification.Using generalized convexity,a sufficient condition for the(weak)quasi ?-efficient solution of nonconvex multiobjective semi-infinite programming problem is established.Then,a new hybrid dual model is introduced to the semi-infinite multiobjective programming problem.Finally,using generalized convexity,approximate weak strong and inverse duality theorems for mixed duality problems of nonconvex semi-infinite multiobjective programming are established,and examples are given to illustrate the rationality of corresponding results.