A Trust Region-Line Search Method Using PSB Update

In this paper, we propose a trust region-line search quasi-Newton type method forsolving unconstrained optimization problems. We use PSB update formula to updatethe quasi-newton metrics. When the trust region trial step is not acceptable, we obtaina descent direction for the objective function. We then use an Armijo type line searchto obtain a steplength and determine the next iterate. Under appropriate conditions,we prove the global and superlinear convergence of the method without requirementof the boundedness of the quasi-newton metrics.We then introduce a nonmonotone line search technique to the method and pro-pose a trust region nonmonotone line search method. We also do some numericalexperiments to test the proposed methods. The results also the e?ectiveness of theproposed. Moreover the performance of the nonmonotone type method performs bet-ter.