Applying Powell's symmetrical technique to conjugate gradient methods

A new conjugate gradient method is proposed for applying Powell's symmetrical technique to conjugate gradient methods in this paper, which satisfies the sufficient descent property for any line search. Using Wolfe line searches, the global convergence of the method is derived from the spectral analysis of the conjugate gradient iteration matrix and Zoutendijk's condition. Based on this, two concrete descent algorithms are developed. 200s numerical experiments are presented to verify their performance and the numerical results show that these algorithms are competitive compared with the PRP + algorithm. Finally, a new explanation of the relationship between conjugate gradient methods and quasi-Newton methods is discussed.