Duality Theories Of Three Kinds Of Nonconvex Optimization Problems

In this paper,we study duality theories of DC optimization problem,composite DC optimization problem and quasiconvex optimization problem.This paper is divided into five chapters.In the first chapter,the research background and the main conclusions for three kinds of optimization problems are introduced.In the second chapter,we provide some notations,conceptions and lemmas.In the third chapter,we study duality theories of a class of special DC optimization problem.Some new constraint qualifications were introduced by using the epigraph technique and the subdifferential property.And the weak duality,the strong duality,the total duality,the stable strong duality and the stable total duality between DC optimization problem and its dual problem were established.In the fourth chapter,we study duality theories of the composite DC optimization problem.By using the epigraph technique and the subdifferential property,some new constraint qualifications are introduced.Under these constraint qualifications,the weak duality,the strong duality,the total duality,the stable strong duality and the stable total duality between composite DC optimization problem and its two dual problems are established.In the fifth chapter,we study duality theories of the quasiconvex optimization problem which constraint functions are quasiconvex function.By using the definition of the generator,the epigraph technique and the subdifferential property,some new constraint qualifications are introduced.Under these constraint qualificationst the strong duality,the total duality,the stable strong duality and the stable total duality between quasiconvex optimization problem and its Lagrange dual problem are established.