A Transformation Function Method For (Solving) Constrained(Nonlinear) Global Optimization (Problems)

Global optimization is a very widely used discipline, which structures to solve the optimal solution of the objective function calculation method, studies the theory and practical application of these methods, and discusses the optimal decision problem. Many economic and management, science and technology, engineering and transportation problems are dependent on the global optimization problem. Now it has developed into an independent branch in the optimization field. In recent decades many new approaches for global optimization have been proposed, such as interval method, integral-level set method, the filled function method and the transformation function method. Belongs to deterministic algorithm in a transformation function method, it by constructing a nature and the function form is not the same new function, at a local minimum point of the original problem existing minimization, for initial point iteration points to leave the original area to get a better than the local minimum points, alternately repeatedly until you find the global minimum point. The core of this article research is for solving nonlinear global optimization problem with constraints of transformation function method.This article consists of four chapters, in the first chapter studies the global optimization problem and several typical global optimization algorithm, introduces some related definitions and properties, providing theoretical basis for the following chapter. The second chapter presented a new transformation function P(x,x*). Proves that the nature of the transformation function, can use the new function to find the global minimum point of the original problem P(x,x*). Building a new algorithm based on these properties, and the real example is given for the numerical experiment. In the third chapter, in view of the transformation function P(x,x*) is proposed in the previous chapter, given different form, the higher precision of the transformation function of Q(x,x*), then through the example of numerical experiment shows that the Q(x,x*) is feasible and effective. The fourth chapter of this paper put forward two new changes of the function to make a summary.