Globally Convex Filled Function Method For Nonlinear Global Optimization Problem

Optimization is a popular subject. Its main work is to discuss the optimiza-tion methods, to construct algorithms for finding the minimum or maximum and to research the theoretical characteristics and computational performance of the algorithms. Optimization problems appear in numerous fields so they are increas-ingly noted by scientists. currently, thanks to the fast development of computer and mathematicians'hard work, the capability of theoretic analysis and practical com-putation are enhanced dramatically. In terms of global optimization, how to find a global minimum and how to judge a global minimum are two difficult subjects. Among all kinds of methods about optimization problems, filled function method is a classical one.Integer programming, which is exactly emphasized by scientists in this day and age, is an important branch of nonlinear programming. It is a kind of common but complicated problem in mathematic programming. The algorithms about solving nonlinear integer programming can be divided into two classes, one is stochastic al-gorithm based on Monte-Carlo method, the other one is certain algorithm. However, both algorithms can just find local minimum, so new algorithms should be designed to combat the global optimization of the nonlinear integer programming.Mixed-integer programming is a new kind of nonlinear programming mixed with integer programming and continuous programming. The problem which include real variables and discrete variables is called nonlinear mixed-integer programming. The appearance of nonlinear mixed-integer programming generally become a serious challenge for mathematic programming researchers. So far, there is almost no proper algorithm about general nonlinear mixed-integer programming. In this paper, we try to discuss nonlinear mixed-integer programming in theory and algorithm and explore some algorithms about solving nonlinear mixed-integer programming though expanding some developed algorithms. We hope that we can offer a new idea to solve the nonlinear mixed-integer programming.The rest of this paper is organized as follows. In Chapter 2, we discuss about unconstrained continuous nonlinear programming. In Chapter 3, we present three algorithms about obtaining local minimum of nonlinear integer programming and then propose a filled function method for nonlinear integer optimization. In Chapter 4, nonlinear mixed-integer programming is discussed and a filled function method for resolving it is provided.