Some Improvements On Nonmonotone Conjugate Gradient Algorithm Based On Trust Region Technique

This thesis studies the conjugate gradient algorithm combining trust region technique with nonmonotone line search technique,the main content of the thesis is presented as follows:In Chapter 1,We briefly introduce the development status of conjugate gradient method and the main results obtained in this thesis.In Chapter 2,Based on modified quasi-Newton equation and simple quadratic function model,a new nonmonotone trust region algorithm for solving unconstrained optimization problems is presented by combining with Gu N.Z.strategy.The global convergence property of the algorithm is proved.Under some reasonable conditions,it is proved that the algorithm is superlinear convergent.The numerical experiments show that the new method is effective.In Chapter 3,Based on trust region technique and modified Quasi-Newton equation,a new nonmonotone nonlinear conjugate gradient method for efficiently solving large scale unconstrained optimization problems is established by combining Zhang H.C.strategy and Gu N.Z.strategy.The global and linear convergence properties of the new method are analyzed.The new method has stable convergence and simple computation,so as to solve the ill-posed and large scale problems.Numerical examples show that the new method is more effective than the methods combined with one nonmonotone strategy.In Chapter 4,Based on Yu Z.S.rule,a new modified PRP conjugate gradient method combining the PRP method with trust region subproblem for solving largescale unconstrained optimization problems is presented.The new method can satisfy the sufficient descent conditions without any line search technique.The global convergence and linear convergence rate of the new method are proved under weaker conditions.Numerical results show that the new method is more effective than several classical conjugate gradient method based on Yu Z.S.rule.