| Conjugate gradient method(CGM)has the advantages of simple algorithm,easy programming,and small storage requirements,so it is widely used to solve large modular optimization problems.In this paper,the conjugate gradient method with restart step is used to solve unconstrained optimization problems and bounded constrained optimization problems.The specific content mainly includes two parts.In the first part,for the unconstrained optimization problem,to improve the computational efficiency of Fletcher-Reeves(FR)and Dai-Yuan(DY)methods,different restart conditions are set according to the conjugate parameters in the search direction,and the restart directions with sufficient descent are designed,and then two conjugate gradient methods with restart steps are proposed.Under general assumptions,their step sizes are obtained by using weak Wolfe line search,and it is proved that the proposed method satisfies global convergence.Then,the proposed algorithm is applied to solve the medium-scale unreduced beam optimization problem and image restoration problem,and compared with similar methods which are recognized to have better numerical results.Experimental results show that the proposed algorithm is effective both in solving unconstrained optimization problems and in image restoration.The second work of this paper,for the nonlinear bounded constraint optimization problem,the active variables are updated according to the active set recognition technique proposed by Facchinei,J ′udice et al,and the conjugate gradient method with restart is used to update the free variables,so as to solve the large-scale bounded constraint problem.Under the condition of strict complementarity,each iteration of the proposed algorithm generates feasible points,and the sequence of objective function values decreases monotonically.Finally,numerical experiments show the effectiveness of the new algorithm in solving large-scale bounded constraint problems. |
