{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T21:10:14Z","timestamp":1700255414729},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2002,10,30]],"date-time":"2002-10-30T00:00:00Z","timestamp":1035936000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2003,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The search direction in unconstrained minimization algorithms for large\u2010scale problems is usually computed as an iterate of the preconditioned) conjugate gradient method applied to the minimization of a local quadratic model. In line\u2010search procedures this direction is required to satisfy an angle condition that says that the angle between the negative gradient at the current point and the direction is bounded away from \u03c0\/2. In this paper, it is shown that the angle between conjugate gradient iterates and the negative gradient strictly increases as far as the conjugate gradient algorithm proceeds. Therefore, the interruption of the conjugate gradient sub\u2010algorithm when the angle condition does not hold is theoretically justified. Copyright \u00a9 2002 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.305","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T10:01:14Z","timestamp":1053597674000},"page":"323-334","source":"Crossref","is-referenced-by-count":1,"title":["An increasing\u2010angle property of the conjugate gradient method and the implementation of large\u2010scale minimization algorithms with line searches"],"prefix":"10.1002","volume":"10","author":[{"given":"Yu\u2010Hong","family":"Dai","sequence":"first","affiliation":[]},{"given":"Jos\u00e9 Mario","family":"Mart\u00ednez","sequence":"additional","affiliation":[]},{"given":"Jin\u2010Yun","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2002,10,30]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"199","article-title":"Theory of algorithms for unconstrained optimization","author":"Nocedal J","year":"1991","journal-title":"Acta Numerica 1992"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.049.044"},{"key":"e_1_2_1_4_2","volume-title":"Matrix Computations","author":"Golub GH","year":"1989"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0906042"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01583777"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/0720042"},{"key":"e_1_2_1_8_2","unstructured":"BirginEG Mart\u00ednezJM.Large\u2010scale active\u2010set box\u2010constrained optimization method with spectral projected gradients. Technical Report University of Campinas S. Paulo Brazil 2001."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01183013"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592055"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6048-6"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.305","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T20:29:59Z","timestamp":1700252999000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,10,30]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2003,6]]}},"alternative-id":["10.1002\/nla.305"],"URL":"https:\/\/doi.org\/10.1002\/nla.305","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,10,30]]}}}