Filled Function Methods For Nonlinearly Global Optimization

The optimization is a widely used discipline, which discusses the characters of optimal choice on decision problems and constructs computing approaches to find the optimal solution. Due to the advancement of society and the development of science and technology, the optimization problems are often discovered in the field of economic planning administration, engineering design, production management, traffic transportation, national defence and so on. They are so important that meet with much recognition With the speedy development of computer and the hard work of scientists, the theoretic analysis and computational methods on optimization have been highly improved.To find the effective methods for finding the global optimal solutions of a general multi-minimizers function is one of the hot topics. There two difficulties in global optimization. One is how to leave from a local minimizer to a smaller one and the other is how to judge that the current minimizer is global. Global optimization methods can be classified into two groups: stochastic and deterministic methods. The filled function algorithm introduced by Ge and Qin (1987) is one of the well-known and practical methods for settling the first difficulty The main idea of filled function method is: If a local minimizer x* has been found, we can make a filled function, such that iterative sequential points leave the valley in which x* lies to find a better point x' in the lower valley (i.e. f(x') < f(x~*)). Then let x' be a new initial point to search for a better minimizer.In recent years, many kinds of filled functions with parameters have been presented. However, those parameters are too hard to adjust and it is most probable that global optimizers are lost or fake better minimizers are found. Therefore, further research is worthy of continuing on how we can construct filled functions with simple forms, better properties and more efficient algorithms.This paper mainly consists of five chapters. In the first chapter, some methods for global optimization problems are briefly presented, including the new filled function methods and the branch - and - bound methods, the modified tunnelling methods and the integral function methods, and so on.Chapter 2, a new filled function with one parameter is suggested for finding a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Without the Lipschitz continuous condition, a new algorithm is presented according to the theoretical analysis. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.Chapter 3, a novel filled function with one parameter is suggested in this paper for finding a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Two algorithms are presented according to the theoretical analysis. The implementation of the algorithms on several test...