Research Of Unconstrained Optimization Fusion Conjugate Gradient Algorithm And Its Application In ARIMA Model Parameter Estimation

With the rapid development of information technology,large-scale optimization problems are increasing.For solving large-scale nonlinear unconstrained optimization problems,the conjugate gradient method is one of its effective algorithms.The algorithm is widely used due to its simple iteration form,small calculation amount and small storage space.The paper will further analyze and study the conjugate gradient algorithm.Firstly,combining with the conjugate parameter formulas of PRP and PHS algorithms and the search direction formula of NLS-DY algorithm,a new three-term conjugate gradient algorithm PPRP is designed;Combining the advantages of conjugate gradient algorithms PRP,MHS and NLS-DY,another new three-term conjugate gradient algorithm LPRP is given.The two new algorithms satisfy the sufficient descent condition without relying on any line search conditions and direction control parameters.Under the Wolfe-Powell line search criterion,the complete convergence of the two algorithms is proved respectively.The conjugation parameters of their conjugate coefficients are not fixed constants,which can be adjusted to make the numerical effect better.Numerical comparison experiments show that the iteration speed of the two new algorithms are relatively faster.Secondly,based on the two proposed three-term conjugate gradient algorithms,a new fusion conjugate gradient algorithm PPRP-LPRP of PPRP and LPRP algorithms is designed.The fusion algorithm is constructed by convex combination of two three-term conjugate gradient algorithms PPRP and LPRP.It has the advantages of two algorithms PPRP and LPRP.At the same time,the new algorithm is more efficient by adjusting the convex parameters.Finally,the new three-term conjugate gradient algorithms PPRP、LPRP and the fusion conjugate gradient algorithm PPRP-LPRP of PPRP and LPRP algorithms are applied to the parameter optimization estimation of time series prediction ARIMA model.PPRP-ARIMA,LPRP-ARIMA,and PPRP-LPRP-ARIMA models are designed by using new algorithms to deal with the parameter estimation problems of ARIMA model.Through three specific examples,the feasibility of the three model fittings and the significant effect of prediction are verified respectively.