The Hybrid Dogleg Method And The Linear Convergent Rate Of Algorithm TR

The trust region method is a kind of efficient and robust ways to solve the ordinary unconstrained optimization problem. And how to solve the subproblem is the critical part of this method. Based on the work of Powell, Dennis and Zhao Yingliang, the first part of this thesis puts forward the hybrid method to solve the subproblem. It is applied to deal with the ordinary unconstrained optimization problem. The convergence of that method and numerical experiments are presented. At the beginning of the second part of this thesis, some basic theories on the nonsmooth problem are given. Then Algorithm TR advocated by Qi Liqun, a kind of nonsmooth trust region methods, is listed. At last the linear convergence rate of Algorithm TR is proofed.