Improvement Of Conic-Model Trust Region Method For Nonlinear Optimization

In this paper, we propose three conic-model trust region methods for nonlinear unconstrained optimization. The main content of the thesis is presented as follows:In chapter two, based on a simple model of the conic-model trust region sub-problem and combine a new strategy of adjust trust region radius, we propose a self adaptive conic-model trust region method for unconstrained optimization. Convergence properties and superlinear convergence of the method are proved under certain conditions. Numerical experiments show that the new method is effective.In chapter three, based on the simple conic-model given in chapter two and with non-monotone technology another new self adaptive strategy for adjusting the trust region radius is proposed. Convergence results of the method are proved. Numerical experiments show that the new method is effective, suitable to solve large scale optimization problems.In chapter four, based on the simple model of conic-model trust region method and combine with a line search technique, a new conic-model 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.