Descent Symmetrization of the Dai–Liao Conjugate Gradient Method

Saman Babaie-Kafaki and Reza Ghanbari ()
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Saman Babaie-Kafaki: Faculty of Mathematics, Statistics and Computer Science, Semnan University, P. O. Box 35195-363, Semnan, Iran
Reza Ghanbari: Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 9177948953, Mashhad, Iran

Asia-Pacific Journal of Operational Research (APJOR), 2016, vol. 33, issue 02, 1-10

Abstract: Symmetrizing the Dai–Liao (DL) search direction matrix by a rank-one modification, we propose a one-parameter class of nonlinear conjugate gradient (CG) methods which includes the memoryless Broyden–Fletcher–Goldfarb–Shanno (MLBFGS) quasi-Newton updating formula. Then, conducting an eigenvalue analysis, we suggest two choices for the parameter of the proposed class of CG methods which simultaneously guarantee the descent property and well-conditioning of the search direction matrix. A global convergence analysis is made for uniformly convex objective functions. Computational experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. Results of numerical comparisons made by the Dolan–Moré performance profile show that proper choices for the mentioned parameter may lead to promising computational performances.

Keywords: Unconstrained optimization; conjugate gradient method; descent condition; eigenvalue; global convergence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:33:y:2016:i:02:n:s0217595916500081

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DOI: 10.1142/S0217595916500081

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