Improvement Of Self Adaptive Trust Region Method For Nonlinear Optimization

In this paper, we propose three self adaptive trust region methods for nonlinear unconstrained optimization. The main content of the thesis is presented as follows:In chapter 2, we propose a self adaptive trust region method for unconstrained optimization based on a simple model of the trust region sub-problem. The simple model needs less memory capacitance and computational complexity. Moreover, according to the ratio between the actual reduction and the predicted reduction of the objective function, we adjust the trust region radius with a new strategy which makes full use of the information at the current point. Convergence properties of the method are proved under certain conditions. Numerical experiments show that the new method is effective.In chapter 3, another new self adaptive strategy for adjusting the trust region radius is proposed. Based on the simple model given in chapter 2, a new non-monotone self adaptive trust region method is presented. During the iterative process, the value of the objective function is allowed to be non-monotone. Convergence results of the method are proved under ? f(x) Lipschitz continuous. Numerical experiments show that the new method is effective.In chapter 4, on the base of the method presented in chapter 2, a new self adaptive trust region method with line search technique is proposed. If the trial step is unsuccessful, the new method doesn't resolve the sub-problem, but obtains the next iteration point by performing a line search technique from the failed point along the trial step. Under some weak conditions, convergence properties are proved. Numerical experiments show that the new method is effective.