A Class Of Step Trust Region Algorithm

Trust region method is a kind of efficient and robust method to solve general unconstrained optimization. Because of its strong convergence, robustness and validity, researchers have paid great attention to it since 1970s. Many kinds of trust region methods, such as quasi-Newton trust region method, nonmonotone trust region method, self-adaptive trust region method have been proposed.In chapter 1, we briefly describe the achievement of unconstrained optimization.In chapter 2, we mainly introduce the trust region method and some related works. Two kinds of nonmonotone trust region methods with line search technique and a class of trust method with linear model are introduced.In chapter 3, a novelty trust region algorithm with line search for unconstrained optimization is presented. The algorithm combine the linear model with the line search. It would reduce the computation because it not only gets decent trial step in every iterate point but also avoids the difficulty of resolving the subproblem repeatedly. Global convergence is obtained under some suitable conditions. Numerical results indicate that the method is effective and practical.In chapter 4, a new trust region algorithm combining linear model and fixed stepsize is proposed, which reduces the numbers of computing function values in the line search algorithm. Under mild conditions, we prove that the global convergence and superlinear convergence of our algorithm under suitable conditions.