Filled Function For Nonlinearly Global Optimization

Optimization studies the characters of optimal choice on decision problems and develops numerical method to find the optimal solution. To find the effective methods for finding the global optimal solution of general multi-minimizers functions is one of the practical methods for the problem. The filled function method (FFM) is one of the practical methods for the problem. This paper mainly concerns the modified filled function methods for nonlinear global optimization problems.This paper mainly consists of five chapters.The first chapter is the introduction. In this chapter, the notions of global optimization and some of its main methods are briefly presented. In the second chapter, the thoughts and the research actuality of the FFM are introduced detailedly.We summarized the research progress of the algorithm, reviewed some classical filled functions and analyses their characteristics. Then, it provided theory basis for further research.In chapter three, a class of filled functions is proposed for solving unconstrained global optimization problems without the Lipschitz continuous,which have only one parameter, it is easy to adjust in numerical calculation and it is better to find minimizers of the global optimization. Theoretical properties of the filled function are investigated, and an algorithm for constrained global optimization problem is developed from the filled function.In chapter four, the idea of filled function for unconstrained global optimization is extended to nonlinear global problems with constraints. Firstly, we give a definition of filled function for constrained problem and under some mild assumptions; we prove it is a filled function. Then, a new algorithm is presented according to the theoretical analysis.The last chapter makes a summarizing analysis and haves a future prospect of the development of the filled function method.