Saddle Point Programming & Fuzzy Saddle Point Programming

In this thesis, several kinds of special optimization methods, such as bilinear saddle point programming, multi-objective saddle point programming, fuzzy saddle point programming, fuzzy multi-objective saddle point programming, etc. , are put forward. The main contents of this thesis are as follows:1. Bilinear saddle point programming and multi-objective saddle point programming are brought forward. After analyzing the optimization conditions of saddle point programming with inequality and equality constraints, the mathematical model of bilinear saddle point programming and its iterative algorithm are given. The thesis also brings forth multi-objective saddle point programming in view of multi-dimensionality and multi-objectivity of decision process in practical world, giving several concepts of its solution at the same time. The thesis also transforms the problem into a single-objective saddle point programming through the weighting method and discusses the relations of their solutions.2. Fuzzy saddle point programming is presented. Considering the substantial existence of fuzzy information and the important status of saddle point programming in practice, the thesis gives fuzzy saddle point programming. According to the characteristics of the mathematical model of fuzzy saddle point programming, the thesis determines the membership function of the fuzzy goal and transforms the model into an ordinary nonlinear programming problem through the generalized fuzzy decision.3. Fuzzy multi-objective saddle point programmings are advanced. The thesis further gives multi-objective saddle point programming with fuzzy parameters and saddle point programming with several fuzzy objectives. Through the method of a -level sets, the former is transformed into an ordinary multi-objective saddle point programming. Through the determined membership functions of fuzzy goals and the generalized fuzzy decision, the latter is transformed into an ordinary nonlinear programming problem. The concept of its solution is also given.