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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
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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
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ͨ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
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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¢   
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SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND
Àà±ð / ·ÖÀà
Ñо¿·½Ïò:Mathematics
Web of Science Àà±ð:Mathematics, Applied; Mathematics
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ÎÄÏ×ÀàÐÍ:Article
ÓïÖÖ:English
Èë²ØºÅ: WOS:000357411200004
ISSN: 1029-242X
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Impact Factor (Ó°ÏìÒò×Ó): Journal Citation Reports®
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Web of Science ºËÐĺϼ¯ÖÐµÄ "ÒýÓõIJο¼ÎÄÏ×": 25
Web of Science ºËÐĺϼ¯ÖÐµÄ "±»ÒýƵ´Î": 0
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