Optimality Conditions And Duality For Multiobjective Fractional Programming Problems

Multiobjective optimization problem is one of the main research fields of optimization theory and applications, Study on which involves many disciplines, such as:convex analysis, nonlinear functional analysis, nonsmooth analysis, and so on. Especially,multiobjective fractional programming problem is a kind of special multiobjective programming problems. And the theory and methods for the multiobjective fractional optimization are widely used in the ares of resource allocation, information transfer, the portfolio problem, etc. In this thesis, we mainly study the theory of Multiobjective fractional optimization in two aspects: Optimality conditions and duality for multiobjective fractional optimization problem. The main results, obtained in this dissertation, may be summarized as follows:1. In chapter 1, we give brief introduction to the development and research significance of multiobjective optimization fractional optimization. And we also summarize the developments of the multiobjective fractional optimization in two aspects associated with this thesis. Finally, we outline the contents studied in this thesis.2. Chapter 2 is committed to study the converse duality for multi-objective fractional programming problems. First, We formulate first-order dual models for the corresponding problem, and discuss converse duality theorems by using Fritz-John type necessary condition, under the weak duality theorems given in some paper without any constraint qualifications. And then, We formulate second-order and higher-order dual models for the corresponding problem, and discuss converse duality theorems by using Fritz-John type necessary condition, under the weak duality theorems given in some paper without any constraint qualifications.3. Chapter 3 studies the optimality conditions and duality for a class of nonsmooth semi-infinite multiobjective fractional programming problems. First, by using equivalent transformation form, We obtain Kuhn-Tucker type necessary conditions, under the constraint qualifications given in some paper. And then, we proved Kuhn-Tucker type su?cient conditions, under the invexity assumption. At last,We formulate Mond-Weir and Wolfe dual models, and obtain duality theorems.