Study On Characterization Of Quasi Approximate Solutions In Multiobjective Optimization Problems

Multiobjective optimization is an interesting research field with many applications,concerning economy,engineering and medicine.In this thesis,we firstly study the op-timality conditions for approximate quasi properly efficient solutions of multiobjective optimization problems,and the sufficient condition for approximate quasi properly effi-ciency of multiobjective optimization problems are studied and generalized further.And then,we study the relations between solutions to the generalized Stampacchia quasi vector variational inequality and the approximate quasi efficient solutions of nonsmooth multi-objective optimization problems.Finally,We consider the relations between solutions generalized vector variational-like inequalities and generalized quasi approximate efficient solutions of nonsmooth multiobjective optimization problems.The main results,obtained in this dissertation,may be summarized as follows:1.In chapter 1,we give brief introduction to the research significance of multiob-jective optimization,And we sum up the development history and current situation of multiobjective optimization.2.In Chapter 2,we study the sufficient condition for approximate quasi properly effi-cient solutions of multiobjective optimization problems,by using the augmented weighted Tchebydicff scalarization problem of multiobjetive optinization problem or the modi-fied weighted Tchdycheff scalarization problem of multiobjective optimizatio problem.we derive a new sufficient condition for approximate quasi properly efficient solutions of multiobjective optimization problems without any convexity conditions.3.In Chapter 3,a multiobjective problem with a feasible set defined by inequality,equality and set constraintts is considered,where the objective and constraint function-s are locally Lipsohitz.a generalized Stampacchia quasi vector variational inequality is formulated as a tool to characterize approximate quasi efficient points or approximate weak quasi efficient points.By using two new classes of generalized convexity func-ticons:approximate quasi psoudoconvex-affine functions and strictly approximate quasi pseudoconvex-affine functions,under suitable constraint qualifications,the relations be-tween Kuhn-Tucker vector critical points,solutions to the multiobjective problem and solutions to the generalized Stampacchia quasi vector variational inequality in both weak and strong forms will be proved.4.Chapter 4 is committed to study the relations between the solutions of generalized vector variational-like inequalities and nonsmooth multi-objective optimization problems under the quasi approximate invexity of high-order assumptions.We derived these con-cepts of quasi approximate efficiency of high order,quasi approximately invex function of high order and quasi approximately pseudoinvex function of high order,we identify the vector critical points,the weakly quasi approximate efficient solution of high order and the solutions of the vector variational-like inequalities under generalized quasi approximate invexity of higher order assumptions.