Study On Improvement And Application Of Nonlinear Conjugate Gradient Method

Nonlinear conjugate gradient method is an important way to solve large-scale unconstrained optimization problems.It has the advantages of simple operation,small storage demand and fast convergence speed.Therefore,the conjugate gradient method is an important research direction.On the basis of previous research,this thesis makes a further improvement on the nonlinear conjugate gradient method,and applies it to the image denoising problem.Firstly,based on the traditional PRP conjugate gradient method,an improved PRP conjugate gradient method is proposed by adding a penalty term to the conjugate parameters.The search direction of the algorithm under the standard Wolfe line search is fully reduced and has global convergence.The results of the numerical test show that the algorithm produced by the improvement of the conjugate parameters is effective and feasible.Secondly,an improved three term mixed conjugate gradient method is given in this thesis.The algorithm can produce a descent direction that is not dependent on any line search technology,and the global convergence of the algorithm is established under the appropriate assumptions.The numerical experiments show that the new three term conjugate gradient method is effective and has some advantages compared with other similar algorithms.Finally,based on the two stage strategy,an improved spectral conjugate gradient method is proposed and applied to the image denoising problem.Under the DL conjugate condition,the sufficient descent of the algorithm is given.The global convergence of the algorithm is proved under the Armijo line search.The results of numerical experiments show the effectiveness of the algorithm,and the denoising effect is more obvious compared with the same algorithm.