Research On Single Parameter Filling Function Method In Global Optimization Problem

In this paper, numerical methods for solving the unconstrained global optimization problems are studied. Two one-parameter filled functions of the smooth and non-smooth unconstrained problems are proposed. If the parameters in the methods are small sufficiently, the functions will show good properties.In the first chapter, the basic theories of the optimization problem are discussed and the definition of the filled function is given.In the second chapter, a one-parameter filled function of the smooth unconstrained optimization problem is proposed. Then a corresponding method is developed. The relevant properties of the filled function are proved which ensure the feasibility and convergence of the method, some typical numerical experiments are calculated with the proposed methods and numerical results show that the methods are feasible and effective.In the third chapter, a one-parameter filled function of the non-smooth unconstrained optimization problem is proposed. Then a corresponding method is developed. The relevant properties of the filled function are investigated which ensure the feasibility and convergence of the method, some typical numerical experiments are calculated with the proposed methods and numerical results show that the methods are feasible and effective.