Robust Approximate Optimality And Duality For A Class Of Uncertain Semi-infinite Optimization Problems

In this thesis,semi-infinite optimization problems with uncertain data are studied.Firstly,the robust approximate duality relationships between an uncertain non-convex semi-infinite optimization problem and its Mond-Weir type duality problem are studied.Secondly,the approximate optimality,duality and saddle point theorems of an uncertain semi-infinite multi-objective optimization problem are studied.In chapter 1,the research background and significance of uncertain semi-infinite programming problems are first described.Then,the optimality and duality of semiinfinite optimization problems are briefly analyzed.Finally,the research motivation and the main content of this thesis are introduced.In chapter 2,the robust approximate duality relationships between an uncertain nonconvex semi-infinite optimization problem and its Mond-Weir type duality problem are studied.Firstly,we introduce a class of nonconvex semi-infinite optimization problems with uncertain data.Then,the Mond-Weir type robust approximation duality problem of this uncertain optimization problem is established,and the duality relationships between them are established.In chapter 3,the optimality,duality and saddle-point theorems of an uncertain semi-infinite multi-objective optimization problem are studied.Firstly,we establish,by using a modified Hybrid scalarization methodology and a new robust type constraint qualification condition,the optimality conditions for weighted robust approximate efficient solutions of the uncertain semi-infinite multi-objective optimization problems.Then,we propose a Wolfe type robust dual problem for this optimization problem and explore robust approximate duality properties between them.Finally,the definition of robust approximate quasi saddle point is given,and then approximate saddle point theorems for the semi-infinite multi-objective optimization problem are described.In chapter 4,the results of this thesis are briefly summarized,and some remaining questions in the future are given.