Study On Robust Solutions And Approximate Solutions For Multiobjective Optimization Problems

The multiobjective optimization problems are the vector extremum problems,that is,maximize or minimize the vector value function under certain conditions.Its theory involves many disciplines,such as convex analysis,nonsmooth analysis,and nonlinear optimization,and is widely used in ecological protection,engineering design and other practical fields.Therefore,the research of multiobjective optimization problems not only promotes the development of relevant discipline theory,but also provides theoretical support for solving practical application problems.This paper mainly study the optimal-ity conditions of the robust and approximate solutions for multiobjective optimization problems and the relationship between the approximate solutions of quasiconvex varia-tional inequalities problems and the approximate solutions of quasiconvex optimization problems.The main results,obtained in this paper,may be summarized as follows:1.In the first part,we study the optimality conditions for the robust solutions.Firstly,we give the relationship between the strict solutions and the robust solutions for the scalar optimization problems.And we also give the optimality conditions of the robust solutions.Then,we derive the relationship between the strict solutions and the robust solutions of the multiobjective optimization problems by using the linear scalarization method,then give the optimality conditions of the robust solutions of the multiobjective optimization problems.2.In the second part,the approximate subdifferentials of quasiconvex function and its applications in quasiconvex optimization problems are studied.We introduce four concepts of approximate subdifferentials based on the existing subdifferentials of the quasiconvex function,and give the relationship among them.And then,we apply these concepts to the quasiconvex multiobjective optimization problems,derive the sufficient conditions and necessary conditions for the approximate weak efficient solutions and the approximate efficient solutions,and give some examples to illustrate the main results3.In the third part,we study the relationship between the approximate solutions of quasiconvex variational inequalities and the approximate solutions of quasiconvex optimization problems.Firstly,we use four kinds of approximate subdifferentials of the quasiconvex function introduced in chapter 3 to give quasiconvex variational inequalities problems.Then,we study the sufficient conditions and necessary conditions for the approximate solutions of quasiconvex variational inequalities and the approximate solutions of quasiconvex optimization problems,and give the corresponding examples.