The Trust Region Method Of MA Model For Solving Nonlinear Programming Problem

The method of moving asymptotes (MA) with trust region technique is a kind of new optimization method which is proposed especially for solving structure optimization problems in engineering. The MA model is often strict convex and separable. The main task of this paper is to extend MA method to solve general nonlinear programming problems. However the generated sub-problem involving an MA model can not be solved efficiently by existing algorithms. By improving the original MA functions, we obtain a continuous and separable sub-problem, and turn this problem into a dual problem which is easily solved. Since the sub-problem is strict convex and separable, the dual problem is especially effective for large scale problem. This work will build a well theoretic and arithmetic foundation for research on new trust region method involving an MA model.In chapter one, basic theory of MA model is introduced. In the following chapter two we give the specific forms of original MA model, the general algorithms and also the extended model. In chapter three, we introduce the improvement of recent MA model concerning on general nonlinear programming, discuss the properties of the improved model and give out the algorithm. The dual sub-problem is given and solved in chapter four. Then we discuss the global convergence of this method in chapter five and give some numerical tests in chapter six. The results show that this MA method with trust region technique is quite effective.