Applications Of Recession Cone And Recession Function In Multiobjective Programming Problems

Multiobjective optimization problem is an important research direction of mathe-matical programming,which not only involves convex analysis and nonlinear analysis and so on,it is also widely used in many fields of business management,information engineering,health and medical community,etc.In view of the theoretical value and practical significance of this topic,this thesis mainly concentrate on the applications of recession cones and recession functions to the multiobjective optimization problems.The main contents of this paper are arranged as follows:Chapter 1 briefly describes the basic concepts of the recession cone and the recession function,illustrates the research significance and contents of the research on the vector optimization problem with the recession cone and the recession function,and summarizes their development history and research status.In Chapter 2,we introduce the recession cone and the unboundedness of a set.Based on the recession properties,the unboundedness of the the function.First,for a nondifferentiable convex function,in term of the recession cone and the classical subdifferential,we study the necessary and sufficient conditions of unboundedness.Then,under generalized convexity assumptions,the generalized recession function is used to characterize the unboundedness.Some extension results are established by adding other conditions.The examples are given to show that the generalized assumptions can not be extent.Finally,we give the application to convex multiobjective optimization problem by using liner scalarization method.Chapter 3 studies the application of the recession cone and the recession function in the nonconvex multiobjective optimization problem.Firstly,we investigate the non-emptiness of the weak efficient solution for unconstrained multiobjective optimization problem based on scalar result.Then,we consider the convexity constrained problem,study the relations between generalized recession cone of epigragh of function and the solution sets.Finally,based on the properties for Hiriart-Urruty nonlinear scalar function,the necessary conditions for existence of several solutions are given.