Duality Theory And Optimality Conditions For DC Robust Optimization Problems

In this paper,we study the duality theory and optimality condition of DC robust optimization problem under the assumptions that the functions are not necessarily lower semicontinuous and the set is not necessarily closed.This paper consists of four chapters.In the first chapter,the research background and the main conclusions for DC robust optimization problem are introduced.In the second chapter,we provide some notations,conceptions and lemmas.In the third chapter,the Farkas lemma and strong duality of DC robust optimization problem are studied.A series of new constraint qualifications are introduced by using the properties of the epigraph of the conjugated function,and the relationships between them are given.The necessary and sufficient conditions for the Farkas lemmas,the stable Farkas lemmas,the strong dualities and the stable strong dualities between the DC robust optimization problem and its dual problem are established.Our results extend the corresponding results in the previous papers.In the fourth chapter,we consider the optimality condition and the total duality of the DC robust optimization problem.Some new constraint quali-fications are introduced by using the subdifferential property of the function.By using those qualifications,the optimality conditions and the stable total dualities for the DC robust optimization problem are given.