Optima And Dulity Of The Nonsmooth Univex In Multiobjective Optimization

Multi-objective optimization problem is an important research field of optimization branch, has the obvious practical background and extensive application fields, such as: social economy, traffic management, engineering design, military defense, management engineering and artificial intelligence, and so on.The method has become an important decision making tool in these areas. In recent decades, the multi-objective optimization theory and methods of research results distinguished, in the theory, many scholars pay close attention to multi-objective optimization problems on the optimality conditions and duality theory, as well as several generalized convexity of research.Convexity is a basic concept in mathematics, in a lot of math problems it plays a very important role, convex optimization has very good characteristics,1. A local minimum is the global minimum,2. Solving complex convex optimization problem can be transformed into a simple solution of the dual problem and so on, but convexity have certain limitation after all, a large number of practical problems does not meet the convexity requirements, so the appropriate relax conditions, the promotion of convex function concept becomes a hot research, thus received a lot of the generalized convexity.The generalized convex function is convex function and the weakening of promotion, when the objective function or restraint function has some generalized convexity, namely is quasi-convex, false convex, constant convex conditions,also can obtain optimal plan of multi-objective solution and efficient solution or weak efficient solutions, also can get some results of accordingly weak duality and strong duality.The main job of this paper:1. The discussion of composite function of the generalized convexity, and prove the composite function in certain conditions pseudo convexity, strictly convex false, the convexity, strict quasiconexities and strong quasiconexities.2.Given the objective function and constraints in(F,α,ρ,θ)-d-v-univex the condition of the sufficient conditions of weak efficient solutions.According to a(F,α,ρ,θ)-d-v nonsmooth generalized convexity of multi-objective optimization of Mond-weir dual, obtained the weak duality theorem and strong duality theorem.This paper is divided into five chapters:the first chapter presents the generalized convex function research background, development situation and the purpose and main content;The second chapter of this paper prepared for related knowledge; The third chapter of composite function is the generalized convexity; The fourth chapter discusses the kind of generalized convex function smooth constant; In chapter5with (F,α,ρ,θ)-d-v -univex nonsmooth generalized convexity of multi-objective optimization of Mond-weir dual, obtained the weak duality theorem and strong duality theorem.