Research On The Filled Function Method For Nonlinear Global Optimization Problem

A study of global optimization problems has become a highly popular topic. Optimization wider spreads in applications such as engineering design, molecular biology, and neural network training. The global optimization problem has two main difficulties: one is how to proceed from a local minimizer to find local minima better; two is how to determine the minimum current is the global optimal solution. Generally, global optimization can be classified into two categories: probabilistic and deterministic methods. Among deterministic algorithms, the filled function algorithm is considered as an effective and practical method which is to solve the first problem. The concept of the filled function method was introduced by Ge in paper [23].The basic idea of the filled function method is to find a global minimizer of a multi-dimensional function called the filled function, which is used to escape the current minimizer in order to find a better minimizer. Because local optimization can be used in the filled function method and the theory and algorithm of local optimization are relatively perfect, the filled function method is very popular with scholars. The key of the filled function is to propose the filled function.This paper is divided into five chapters:The first chapter simply describes the importance of study about the optimization, and then gives some basic definitions about optimization which is necessary for this paper. Then it explains in detail the produced background and the prospects for development of the filled function method which is a study of global optimization problem of determination method, and analyzes the advantages and disadvantages of the filled functions that scholars put forward.The second chapter proposes a new continuous and one parameter filled function for unconstrained optimization problems according to the classic definition [46], based on the premise that objective function is Lipschitz-continuous and gradient, and discusses the properties of the filled function, which overcomes the shortcomings that the filled function has exponential term in [23,46,70] and has not any information of the objective function in [59,72,73].In the third chapter, according to the literature [71], a new definition of [71] is given, which is different from the classical definition in [46]. A new single parameter filled function is proposed and it improves the disadvantage)()(*xfxf ? of the filled function in the literature [71].Chapter 4 gives a two parameter filled function on non-smooth unconstrained global optimization problems. In fact, the function is a one parameter filled function. Compared to the literature [69], the filled function does not contain index.The fifth chapter summarizes the paper and prospects the development of the filled function method.