Study On Scalarizations For Approximate Solutions For Multiobjective Optimization Problems

As an important part of mathematical programming, multiobjective optimization is a promising interdisciplinary research field with many significant applications. Study on which involves many disciplines, such as:convexity analysis, nonsmooth analysis, and so on. And there are many multiobjective optimization problems in economic planning, environmental protection, financial investment, sustainable development of society and other major management decisions. In this thesis, we mainly study nonlinear scalarizations for quasi approximate solutions for multiobjective optimization problems and the optimality conditions for approximate solutions for vector variational inequality problems and some relations between vector 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 also summarize the developments of the multiobjective optimization in two aspects associated with this thesis. Finally, we outline the contents studied in this thesis.2. In Chapter 2, we study the nonlinear Scalarizations for quasi approximate solutions for multiobjective optimization problems. First, we derive several necessary and sufficient conditions for quasi approximate (weak) efficient solutions of multiobjective optimization problems without any convexity conditions by reviewing one standard nonlinear scalarization techniques in general cone sequence. And then, base on two nonlinear scalarization problems, we derive several necessary and sufficient conditions for quasi approximate (weakly, properly) efficient solutions of multiobjective optimization problems without any convexity conditions in natural cone sequence. And using the norm, we derive a kind of nonlinear scalarization problem for quasi approximate efficient solutions of multiobjective optimization problems.3. In Chapter 3, we study the optimality conditions for approximate solutions for vector variat:(?) inequality problems and some relations between vector optimization problems. First, we introduce a new kind of approximate solutions for vector variational inequalities using co-radiant set in Banach spaces, and we studied the optimality condi-tions for the approximate solution. And then, we deals with the relations between this ap-proximate solutions for vector variational inequality problems and approximate solutions for vector optimization problems in n-dimensional Euclidean space. Finally, We consider the relations between solutions for vector variational inequality problems and quasi ap-proximate for vector optimization problems. We identify the vector critical points, the weak quasi approximate efficient solutions and the solutions of the weak vector variational inequality problems under generalized quasi approximate convexity assumptions.