Optimality Conditions And Duality For Multiobjective Optimization

Convexity is an important mathematical concept. For the need of solving practicalproblems, People has generalized the convexity from different point of view. Invexity isan important kind of generalized forms. So,studying the generalized forms of convexityand applications in optimization theory is very important and interesting.This thesisstudy Higher order K-pseudo convex, higher order K-quasiconvex and higher orderK-convex. We consider the optimality conditions and duality for multiobjective underthese generalized convexity assumptions.Chapter1acts as the general introduction to the significance and current situationin the study of the invexity.Chapter2: Higher order cone convex, pseudo convex, strongly pseudo convex,quasiconvex functions and Higher order sufficient optimality conditions are given for aweak minimum,minimum solution of a vector optimization problem under which anobjective function is Higher order K-convex and a constraint function is Higher orderK-convex are introduced by Meetu [17].In the paper, First: Higher order sufficientoptimality conditions are given for a weak minimum,minimum solution of a vectoroptimization problem under which an objective function is Higher order K-pseudoconvex and a constraint function is Higher order K-convex.Second: Higher ordersufficient optimality conditions are given for a weak minimum,minimum solution of avector optimization problem under which an objective function is Higher orderK-pseudo convex and a constraint function is higher order K-quasiconvex.Chapter3: Higher order cone convex, pseudo convex, strongly pseudo convex,quasiconvex functions and weak,strong duality theorems are established for (VP) and(HD) under which an objective function is Higher order K-convex and a constraintfunction is higher order K-convex are introduced by Meetu [17].In the paper, First:weak and strong duality theorems are established for (VP) and (HD) under which an objective function is Higher order K-pseudo convex and a constraint function is higherorder K-convex. Second, weak and strong duality theorems are established for (VP)and (HD) under which an objective function is Higher order K-pseudo convex and aconstraint function is higher order K-quasiconvex.Chapter4comes to a conclusion. In the meanwhile, it put forward some problemsfor further study.In this thesis, main results gather in the2-th,3-th chapter.