Optimality Conditions And Duality For Multiobjective Optimization

Convexity is an important mathematical concept. For the need of solving practical problems, People has generalized the convexity from different point of view.Invexity is an important kind of generalized forms. So,studying the generalized forms of convexity and applications in optimization theory is very important and interesting.This thesis study two kinds of generalized convexity--r-semipreinvex and B-(p,r)-invexity. We consider the optimality conditions and duality for multiobjective under these generalize- d convexity assumptions.Chapter 1 acts as the general introduction to the significance and current situation in the study of the invexity.Chapter 2 consider the optimality conditions and duality for multiobjective progra- mming (MP) under the arcwise directionally differentiable conditions in the r-semipreinvex assumption.Under the assumption of r-semipreinvex, we establish the KKT necessary conditions and the KKT sufficient conditions.Meanwhile,we study the Mond-Weir weak duality, strong duality, deverse duality etc for multiobjective programming.Chapter 3 consider a class of nonsmooth multiobjective programming (NMOP) with equality and inequality constraints, and establish the mixed dual model for this programming; and so discuss the duality theories between the dual problem and the primal problem in terms of Clarke subdifferential, under the assumption of the nonsmoooth B-(p,r)-invxity. And we study the mixed weak duality, strong duality, deverse duality etc for multiobjective programming (MP) under the assumption of r-semipreinvex.Chapter 4 comes to a conclusion.In the meanwhile, it put forward some problems for further study.In this thesis, main results gather in the 2-th,3-th chapter.