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A descent modified Polak-Ribiere-Polyak conjugate gradient method and its global convergence
Authors:Zhang  Li; Zhou  Weijun; Li  Dong-Hui
Institution: 1 Institute of Mathematics, Changsha University of Science and Technology, Changsha 410077, China, 2 College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
Abstract:** Email: zl606{at}tom.com*** Corresponding author. Email: weijunzhou{at}126.com**** Email: dhli{at}hnu.cn In this paper, we propose a modified Polak–Ribière–Polyak(PRP) conjugate gradient method. An attractive property of theproposed method is that the direction generated by the methodis always a descent direction for the objective function. Thisproperty is independent of the line search used. Moreover, ifexact line search is used, the method reduces to the ordinaryPRP method. Under appropriate conditions, we show that the modifiedPRP method with Armijo-type line search is globally convergent.We also present extensive preliminary numerical experimentsto show the efficiency of the proposed method.
Keywords:PRP method  MPRP method  Armijo-type line search  global convergence
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