Global Optimization To Improve The Filled Function Method

With the rapid development of the computer science and its technology, the global optimization problem has become one of the most important research fields in connection with the theory and algorithms for optimization. Recently, the filled function method is one of the effective approaches for global optimization. This thesis studies some issues on filled function method.In the first chapter, we introduce a filled function. Furthermore, a class of mitigators is defined, which may reduce the negative definite effect of the Hessian of a filled function. Results of numerical experiments on testing program shows it's a better property.In the second chapter, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduce a new modified function and construct a corresponding optimization subproblem with one constraint. Then, we obtain a better local optimal solution by applying a local search method to the one-constraint optimization subproblem. A termination rule is obtained which can serve as stopping criterion for the iterating process.In the third chapter, a new auxiliary function method is proposed, and then a stretching function technique is used to modify the objective function with respect to the obtained local minimum. Next, an auxiliary function is constructed on the stretched function, which always descends in the region where the function values are higher than the obtained minimum, and it has a stationary point in the lower area. The main feature of the new method is that it relaxes significantly the dependency for the parameters. Numerical experiments show that the new algorithm has a more rapid convergence.