Filled Function Methods And An Interval Algorithm For Global Optimization Problems

This thesis is devoted to two global optimization algorithms, such as a filled function method and an interval algorithm. Their properties and extended applications are discussed on emphasis and the satisfactory results are achieved. The main work of the dissertation can be summarized as follows:Based on some existing filled function methods in the references, a modified filled function method with two adjustable parameters is constructed for nonsmooth optimization. This method is simple and feasible. Theoretical analyses and a large amount of numerical results show that this method is better than other methods in the aspects such as accuracy, runtime and iterative number.The filled function with two parameters has some disadvantages, especially, the excessive restriction on the choices of the parameter values. So a modified filled function with only one parameter is proposed with much improved performance for a Lipschitz programming. Numerical experiments show that the method is efficient.This paper deals with the transformation of a multiple objective programming into a single objective programming. By the character of the single objective programming, a novel filled function method is described. Global optimal solutions of the single objective programming are obtained by the method, i.e., the minimal weakly efficient solutions to the original programming. The numerical tests show that it is practical and effective. Moreover, our filled function guarantees its minimum to be always achieved at a point where its function value is not higher than the function value of the current minimum.Besides all of the above, as to a discrete minimax problem, the interval extension of objective function and region deletion test rules are discussed via quasi-partial derivative. An interval algorithm is described based on the bisection rule of Moore. Theoretical analyses and numerical results show that the algorithm is efficient and that all global optimal points can be found in the given accuracy.