{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T15:35:01Z","timestamp":1773848101609,"version":"3.50.1"},"reference-count":40,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2006,3,1]],"date-time":"2006-03-01T00:00:00Z","timestamp":1141171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2006,3]]},"abstract":"<jats:p>\n            Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition\n            <jats:bold>g<\/jats:bold>\n            <jats:sup>T<\/jats:sup>\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sub>\n            <jats:bold>d<\/jats:bold>\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sub>\n            \u2264 \u22127\/8 \u2016\n            <jats:bold>g<\/jats:bold>\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sub>\n            \u2016\n            <jats:sup>2<\/jats:sup>\n            and which is globally convergent whenever the line search fulfills the Wolfe conditions. This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.\n          <\/jats:p>","DOI":"10.1145\/1132973.1132979","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"113-137","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":350,"title":["Algorithm 851"],"prefix":"10.1145","volume":"32","author":[{"given":"William W.","family":"Hager","sequence":"first","affiliation":[{"name":"University of Florida, Gainesville, FL"}]},{"given":"Hongchao","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of Florida, Gainesville, FL"}]}],"member":"320","published-online":{"date-parts":[[2006,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1093\/imanum\/5.1.121","article-title":"Decent property and global convergence of the Fletcher-Reeves method with in exact line search","volume":"5","author":"Al-Baali M.","year":"1985","unstructured":"Al-Baali , M. 1985 . 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