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ÌâÄ¿£ºThree modified Polak-Ribi¨¨re-Polyak conjugate gradient methods with sufficient descent property ×÷ÕߣºMin Sun1* and Jing Liu2 ÔÓÖ¾£¬Ä꣬ÎÄÕÂÐòºÅ£ºJournal of Inequalities and Applications 2015, 2015:125 |
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Three modified Polak-Ribiere-Polyak conjugate gradient methods with sufficient descent property ×÷Õß:Sun, M (Sun, Min)[ 1 ] ; Liu, J (Liu, Jing)[ 2 ] JOURNAL OF INEQUALITIES AND APPLICATIONS ÎÄÏ׺Å: 125 DOI: 10.1186/s13660-015-0649-9 ³ö°æÄê: APR 8 2015 ²é¿´ÆÚ¿¯ÐÅÏ¢ ÕªÒª In this paper, three modified Polak-Ribiere-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, 2007), 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 searches. 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. ¹Ø¼ü´Ê ×÷Õ߹ؼü´Ê:conjugate gradient method; sufficient descent property; global convergence KeyWords Plus:SCALE UNCONSTRAINED OPTIMIZATION; GLOBAL CONVERGENCE; LINE SEARCH ×÷ÕßÐÅÏ¢ ͨѶ×÷ÕßµØÖ·: Sun, M (ͨѶ×÷Õß) Zaozhuang Univ, Sch Math & Stat, Beian St, Zaozhuang 277160, Peoples R China. µØÖ·: [ 1 ] Zaozhuang Univ, Sch Math & Stat, Zaozhuang 277160, Peoples R China [ 2 ] Zhejiang Univ Finance & Econ, Sch Math & Stat, Hangzhou 310018, Zhejiang, Peoples R China µç×ÓÓʼþµØÖ·:ziyouxiaodou@163.com »ù½ð×ÊÖúÖÂл »ù½ð×ÊÖú»ú¹¹ ÊÚȨºÅ Shandong Province outstanding young teachers in higher schools foundation of Scientific Research Project of Shandong Universities J13LI03 Shandong Province Statistical Research Project 20143038 ²é¿´»ù½ð×ÊÖúÐÅÏ¢ ³ö°æÉÌ SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND Àà±ð / ·ÖÀà Ñо¿·½Ïò:Mathematics Web of Science Àà±ð:Mathematics, Applied; Mathematics ÎÄÏ×ÐÅÏ¢ ÎÄÏ×ÀàÐÍ:Article ÓïÖÖ:English Èë²ØºÅ: WOS:000357411200004 ISSN: 1029-242X ÆÚ¿¯ÐÅÏ¢ Ŀ¼£º Current Contents Connect® Impact Factor (Ó°ÏìÒò×Ó): Journal Citation Reports® ÆäËûÐÅÏ¢ IDS ºÅ: CM1AF Web of Science ºËÐĺϼ¯ÖÐµÄ "ÒýÓõIJο¼ÎÄÏ×": 25 Web of Science ºËÐĺϼ¯ÖÐµÄ "±»ÒýƵ´Î": 0 |

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