Trust Region Algorithms For Constrained Nonlinear Optimization Problems

Trust region method is a class of important numerical algorithms for nonlinear optimization. There are strong convergence and reliability properties for these algorithms, so they are widely used in many fields. In this thesis we discuss trust region algorithms for constrained nonlinear optimization problems by three chapters. In chapter one,we briefly introduces the development of trust region method and the main contents of this paper. A trust region algorithm for special linear inequality constrained optimization problems is proposed in chapter two. This algorithm is based on the interior-point method. In constructing the subproblem, we move the nonnegative bound constraints from the general inequality ones into the trust region constraints, and obtain a solved-easily subproblem. Under very mild conditions, convergence results for the algorithm are given and numerical results are reported. In the last chapter, we present three modified trust region algorithms for general nonlinear constrained optimization problems. For these algorithms we choose exact penalty function as the merit function and modify the rules for accepting the trial step. Global convergen- ce for these algorithms are proved and numerical results are reported in this chapter.