Several New Spectral Conjugate Gradient Methods

Spectral conjugate gradient method is a new algorithm which synthesizes the advantages of spectral gradient method and conjugate gradient method.It is one of the most commonly used and effective methods to solve large-scale unconstrained optimization problems.It is also the research and application hotspot for optimization theorists and optimization practitioners.Based on the existing literature and the classical nonlinear spectral conjugate gradient method,three different forms of spectral conjugate gradient method are constructed in this paper The specific work is as followsFirstly,inspired by the conjugate direction control parameters constructed by Wang and Shan,this paper proposes a new conjugate parameter formula,selects the appropriate spectral coefficient,and ensures that the algorithm constructed on this basis meets the conjugate condition under any line search,and then the search direction generated during iteration is fully reduced The global convergence of the method is verified by Wolfe line search.Secondly,inspired by AZPRP method and YHM method,a new parameter is introduced and a new class of mixed spectral conjugate gradient method is proposed The new algorithm inherits FR,PRP,LS,HS,DY,CD method has the advantages of generating a descent direction independent of any line search,and has good convergence performance under the condition of strong Wolfe line search Through a set of test functions,compared with AZPRP method,the results show that the algorithm in this paper is more effective.Finally,combined with some characteristics of Li’s improved trinomial spectral conjugate gradient method and the excellent theoretical properties of quasi Newton method,using two parameters constructed by sun for reference,an appropriate spectral parameter is calculated by using an improved crosscutting condition A spectral conjugate gradient method based on Quasi Newton equation is proposed.The new algorithm can always decline automatically in each iteration.Numerical results show that the algorithm is superior to SSML-BFGS method and IFR method,and is effective and stable.