Global Optimization Studies Of The Auxiliary Function Method

Global optimization addresses the computation and characterization of global solutions to nonlinear function. The main task of global optimization is to determine (with theoretical guarantees) an approximate global optimal solution of the objective function with a set of constraints or unconstraint.Due to the development of science and technology, the global optimization problems are often discovered in the field of economic planning administration, engineering design, production management, traffic transportation, national defenses and so on. It has attracted extensive attention. The auxiliary function method for global optimization have been extended and improved in this paper.This paper contains three chapters:In the first chapter, several basis concepts and characters on generally nonlinear programming are introduced. Then some typical methods for global optimization problems are briefly presented.In the second chapter, a new filled function method on solving global optimization problems without constraint is introduced. A new filled function for solving general unconstrained optimization problem and its feasible filled function algorithm are given, the nature of the function is analyzed. Numerical experiments verified the effectiveness of the algorithm.In the third chapter, a novel cut-peak function method and "stretching" function algorithm for the global optimization problems closed with box-constraint are mainly introduced. The implementation procedure of the two algorithm is compared by graphics and a new auxiliary function is established based on it. The algorithm integrated both sides'thought and is easy to be made.