Applying Powell's symmetrical technique to conjugate gradient methods

Authors:
Liu Dongyi;Xu Genqi
Affiliations:
Department of Mathematics, Tianjin University, Tianjin, P.R. China 300072;Department of Mathematics, Tianjin University, Tianjin, P.R. China 300072
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

A new conjugate gradient method is proposed by applying Powell's symmetrical technique to conjugate gradient methods in this paper. Using Wolfe line searches, the global convergence of the method is analyzed by using the spectral analysis of the conjugate gradient iteration matrix and Zoutendijk's condition. Based on this, some 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 brief discussion of the new proposed method is given.