{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:55Z","timestamp":1740134515867,"version":"3.37.3"},"reference-count":31,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61373174"],"award-info":[{"award-number":["61373174"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent condition<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msubsup><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:msubsup><mml:msub><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo>\u2264<\/mml:mo><mml:mo>-<\/mml:mo><mml:mfenced separators=\"|\"><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo>-<\/mml:mo><mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mrow><mml:mfenced separators=\"|\"><mml:mrow><mml:mn mathvariant=\"normal\">4<\/mml:mn><mml:msub><mml:mrow><mml:mi>\u03b8<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:mfenced><mml:msup><mml:mrow><mml:mfenced open=\"\u2225\" close=\"\u2225\" separators=\"|\"><mml:mrow><mml:msub><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>\u2009<\/mml:mo><mml:mo>\u2009<\/mml:mo><mml:mfenced separators=\"|\"><mml:mrow><mml:msub><mml:mrow><mml:mi>\u03b8<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mrow><mml:mn mathvariant=\"normal\">4<\/mml:mn><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:mfenced><\/mml:math>and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.<\/jats:p>","DOI":"10.1155\/2014\/825958","type":"journal-article","created":{"date-parts":[[2014,1,8]],"date-time":"2014-01-08T16:23:17Z","timestamp":1389198197000},"page":"1-14","source":"Crossref","is-referenced-by-count":1,"title":["Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4694-0140","authenticated-orcid":true,"given":"San-Yang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Yuan-Yuan","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xidian University, Xi\u2019an 710071, 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