Solution Nonmonotone Trust Region Method For Constrained Optimization, And Perry-shanno 's Memory Quasi-newton Method

In this paper, we propose three methods for unconstrained optimiza-tion.(1).a new nonmonotonic self-adaptive trust region algorithm without resolv-ing the subproblem.(2). nonmonotonic Perry-Shanno Memoryless Quasi-Newtonmethod.(3).nonmonotonic Perry-Shanno Memoryless Quasi-Newton method with pa-rameter, the dissertation can be summarized as follows:1. Paper [2] proposes a self-adaptive trust region algorithm, and the formula oftrust region radius is△_k+i= R_c2(r_k)‖d_k‖.Where R_η(t) names R-function.wepropose a new R-function which is simpler than Paper [2],and define a formula△_k+1= R_c2(r_k)△_k as trust region radius, when a trial step is accepted,sometimesd_k is a good descend direction,we take a inexact line search to obtain x_k+1.When atrial step is not accepted,the method does not reslove the subproblem but generatesa iterative point whose steplength is defined by a formula.Under mild conditions,weprove that the algorithm is global convergence.Numerical results are presented whichshow that the method is effective. Numerical results are also presented.2. This chapter will try to discuss nonmonotonic Memoryless Quasi-Newtonmethod.The convergence of this method is proved for convex function and non-convex function. Primary numerical results demonstrate that the algorithm is efficient.3. The chapter takes nonmonotonic Perry-Shanno Memoryless Quasi-Newtonmethod with parameter. The convergence of this method is proved for convex functionand non-convex function.Preliminary numerical experiments show that the proposedalgorithm is effective.