The Optimality Conditions For Multiobjective Programming Problems

Multiobjective programming as an important research directions in mathematical programming,Study on which involves many disciplines,such as:convexity analysis,nonsmooth analysis,and so on.In particular,the semi-infinite multiobjective program-ming problem as a special problems has been widely used in engineering design,The field of economic balance,management science,information technology,etc.In this thesis,we mainly study optimality conditions for quasiconvex multiobjective programming probems and optimality conditions for semi-infinite programming problems.The main results,obtained in this dissertation,may be summarized as follows:1.In chapter 1,we give brief introduction to the research significance of multi-objective programming problem?quasiconvex programming problem and semi-infinite programming problem.And we also summarize the developments of above these prob-lems.Finally,we outline the contents studied in this thesis.2.In Chapter 2,we study the optimality conditions for quasiconvex multiobjective programming problems.First,we use differential as a tool study the weak efficient solutions?efficient solutions and properly efficient solutions for quasiconvex multiobjec-tive programming problems which constraint set is convex and the objective function is quasiconvex.And then,base on optimality conditions for quasiconvex programming problems,we derive several optimality conditions for quasiconvex multiobjective pro-gramming problems.3.In Chapter 3,we study the optimality conditions for semi-infinite programming problems.First,we study a class of nonsmooth semi-infinite programming problems that objective functions and constraint functions which are locally Lipschitz in convex subset C of Rn.Based on optimality for nonsmooth semi-infinite fractional programming problems,under certain constraint,we derive necessary optimality conditions for nonsmooth semi-infinite programming problems with abstract set c.And then,we study the semi-infinite multiobjective programming problems that objective functions and constraint functions which are locally Lipschitz,under certain constraint,we derive strong type KKT necessary optimality of nonsmooth semi-infinite multiobjective programming problems.