Research On The Filled Function Methods For Nonlinear Global Optimization

Many recent advances in science, economics and engineering rely on numerical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily diverse and they include economic modelling, finance, management, networks and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering and so on.During the past four decades, many new theoretical, algorithmic, and computational contributions have helped to solve global optimization problems arising from important practical applications. The filled function method proposed in the 1990s is among the contribution list.The filled function and the filled function method was first proposed by Renpu Ge. Its basic idea is by constructing auxiliary functions, namely the filled function, to find global solutions of original objective function step by step.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 simpler forms, better properties and more efficient algorithms.This dissertation mainly concerns the modified filled function methods for nonlinear global optimization problems. It consists of five chapters.In the first chapter, global optimization problems and some of its main methods are briefly introduced. In the second chapter, the definition of the filled function for continuous global optimization in paper [31] is modified and a new filled function is presented. New filled functions are required to have local minimizers instead of being minimized on the line segment, which is very important and meaningful to reach a global solution successfully. In chapter three, a definition of the filled function for nonlinear integer programming problem, which is modified from that of the globally convexized filled function in paper [33], is given. A filled function satisfying the definition is presented, which is modified from that of the box constrained continuous...