The Research On Several Kinds Of Trust Region Algorithms

Linear search methods and trust region methods are two most important algorithms to the optimization problems. The key constitute parts of them are search direction and trust region subproblem respectively. Another important part is naturally the framework themselves. In this paper, we focus on improving the sloving of the trust region subproblem by introducing the self-adaptive idea and the framework by using some new strategys such as nonmonotone technology and filter technique. Then we analyse the convergence of the improved algorithms under certain conditions and examine their practical computing result by many experiments.In chapter 1, we briefly introduce the achievement of trust region method and our main research. Then we introduce the self-adaptive idea, the nonmonotone technology and filter technique.From chapter 2 to chapter 4, we mainly consider the trust region method of unconstrainted optimization problems. Based on the traditional trust region method, we first give the nonmonotone self-adaptive trust region algorithm and its improvement, then introduce the nonmonotone filter self-adaptive trust region algorithm. Laterly, we prove the convergence of the improved algorithms under certain conditions and report the results of these new algorithms on some unconstrained optimization problems. All the results show that our improved algorithms are better than the traditional trust region method in efficiency of the practical computing.In chapter 5, we extend the nonmonotone technology and filter technique to the optimization problems with equality constrainted. Because the pure filter technique can not get rid of Maratos effect completely, we try to judge the acceptance of trial point by nonmonotone filter technology. In the aspect of the trial step, we compute a quasi-normal step and a tangential step to get it instead of solving the trust region subproblem. Lastly, we analyse the convergence of the improved algorithms under certain conditions.