| The semi-infinite multiobjective programming problem is an optimization problem in which the objective function is a vector value and the number of constraint functions is infinite.In recent years,the semi-infinite multiobjective programming problem has become a new research hotspot in mathematical programming,because the semi-infinite multiobjective programming problem has been widely used in financial investment,economic analysis,military decision-making,engineering design,and ecological protection.In this paper,the strong KKT condition,duality theorem and saddle point theorem for approximate solutions of nonsmooth semi-infinite multiobjective programming problems are studied by using tangential subdifferentials.The main contents are as follows:The first chapter briefly describes the background and significance of the research on semi-infinite multiobjective programming,then introduces the development status of the optimality condition,duality theory and saddle point,and finally proposes the main research contents of this paper.The second chapter mainly introduces the notation of this paper and the basic concepts and basic theories required for the research.In chapter 3,strong KKT optimality conditions for approximate solutions of semiinfinite multiobjective programming problems are studied.Three kinds of generalized convexity functions and three new regular conditions are defined by using tangential subdifferentials,and strong KKT necessary and sufficient conditions for approximate solutions of semi-infinite multiobjective programming problems are established by using them.In chapter 4,we present two dual models for semi-infinite multiobjective programming: Wolfe type dual and Mond-Weir type dual.For these two kinds of dual problems,two different kinds of approximate solutions are defined,and under generalized convexity conditions,the relationship between approximate solutions of semi-infinite multiobjective programming problems and approximate solutions of corresponding dual problems are established,and approximate weak duality,strong duality and inverse duality theorems are obtained.In chapter 5,the approximation saddle point theorems for semi-infinite multiobjective programming problems are studied.Based on the vector Lagrange function of the semi-infinite multiobjective programming problem,the approximate saddle point is defined.Under generalized convexity,the relationship between approximate solutions and approximate saddle points for semi-infinite multiobjective programming problems is given.Chapter 6 briefly summarizes the main content of this paper,and proposes problems to be further considered and solved in the future. |
PDF Full Text Request