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Three modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property

Min Sun, Jing Liu
2015 Journal of Inequalities and Applications  

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In this paper, three modified Polak-Ribière-Polyak (PRP) conjugate gradient methods for unconstrained optimization are proposed. They are based on the two-term PRP method proposed by Cheng (Numer. Funct. Anal. Optim. 28:1217-1230, the three-term PRP method proposed by Zhang et al. (IMA J. Numer. Anal. 26:629-640, 2006), and the descent PRP method proposed by Yu et al. (Optim. Methods Softw. 23:275-293, 2008). These modified methods possess the sufficient descent property without any line
more » ... s. Moreover, if the exact line search is used, they reduce to the classical PRP method. Under standard assumptions, we show that these three methods converge globally with a Wolfe line search. We also report some numerical results to show the efficiency of the proposed methods.
doi:10.1186/s13660-015-0649-9 fatcat:gyj46mt7kbhjzliuzv5xwvizoi
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Min Sun, Jing Liu. "Three modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property." Journal of Inequalities and Applications 2015.1 (2015)