Applying Powell’s symmetrical technique to conjugate gradient methods

Applying Powell’s symmetrical technique to conjugate gradient methods

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Article ID: iaor20115116
Volume: 49
Issue: 2
Start Page Number: 319
End Page Number: 334
Publication Date: Jun 2011
Journal: Computational Optimization and Applications
Authors: ,
Keywords: optimization, graphs, programming: geometric, matrices
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.

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