Improved Conjugate Gradient Algorithm And Its Application

With the development of the Internet and information technology,more and more largescale optimization problems are faced by human beings.In order to solve such problems,scientists have proposed numerous algorithms.Among them,the conjugate gradient method is one of the more effective methods and widely applied because of its advantages such as simple iterative form,less calculation and storage space.In this dissertation,the existing nonlinear conjugate gradient algorithm is further studied.Firstly,the research progress of optimization algorithms in recent years is reviewed,and the advantages and disadvantages of classical conjugate gradient algorithms are analyzed.A series of improvement work based on optimization algorithms in recent years is evaluated,and the improvement ideas of the algorithm are summarized.Based on these improvements,two new improved algorithms are proposed.The HS algorithm has better numerical performance but slower convergence.Based on the improved ideas of WYL and P-W algorithms,combined with the search direction of NLS-DY algorithm,the JLJH and H-M algorithms are obtained.The search direction generated by the Wolfe-Powell line search satisfies the condition of sufficient descent.numerical experiments show the algorithm have efficient numerical performance.Secondly,combining the advantages of several classical conjugate gradient methods,a hybrid conjugate gradient method is proposed.The WYL algorithm with good numerical effect is combined with the FR algorithm with better convergence,and selected the appropriate convex parameters to ensure that the algorithm satisfies the sufficient descent condition.The NWF conjugate gradient algorithm is obtained,numerical experiments show the stability and efficiency of the algorithm.Finally,new conjugate gradient algorithms are applied to the parameter estimation of the time series model to verify the superiority of the algorithms.The new algorithm is used to solve the parameter optimization estimation problem of ARMA model,and the JLJHARMA,H-M-ARMA and NWF-ARMA models are obtained.In order to verify the rationality and efficiency of the models,the new models are applied to the fitting and prediction of the example models.Numerical examples illustrate the superiority of the models and further illustrate the feasibility of the new algorithms.