{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:59:30Z","timestamp":1753883970555,"version":"3.41.2"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2024,4]]},"abstract":"<jats:p> In this paper, we develop some three term nonlinear conjugate gradient methods based on the Hestenes\u2013Stiefel (HS), the Polak\u2013Ribi\u00e8re\u2013Polyak (PRP) and the Liu\u2013Storey (LS) methods. The proposed algorithms always generate sufficient descent directions which satisfy [Formula: see text]. When the Wolfe or the Armijo line search is used, we establish the global convergence of the proposed methods in a concise way. Moreover, the linear convergence rate of the methods is discussed as well. The extensive numerical results show the efficiency of the proposed methods. <\/jats:p>","DOI":"10.1142\/s0217595923500203","type":"journal-article","created":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T07:12:33Z","timestamp":1684307553000},"source":"Crossref","is-referenced-by-count":2,"title":["Some New Descent Nonlinear Conjugate Gradient Methods for Unconstrained Optimization Problems with Global Convergence"],"prefix":"10.1142","volume":"41","author":[{"given":"Min","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics, Hunan University, Changsha, Hunan, P. R. China"},{"name":"Department of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"S0217595923500203BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623497318992"},{"key":"S0217595923500203BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100263"},{"volume-title":"Practical Method of Optimization, Vol. 1: Unconstrained Optimization.","year":"1987","author":"Flectcher R","key":"S0217595923500203BIB003"},{"key":"S0217595923500203BIB004","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/7.2.149"},{"key":"S0217595923500203BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-014-9687-3"},{"key":"S0217595923500203BIB006","doi-asserted-by":"publisher","DOI":"10.1137\/030601880"},{"key":"S0217595923500203BIB007","first-page":"35","volume":"2","author":"Hager W","year":"2006","journal-title":"Pacific Journal of Optimization"},{"key":"S0217595923500203BIB008","doi-asserted-by":"publisher","DOI":"10.6028\/jres.049.044"},{"key":"S0217595923500203BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.06.034"},{"key":"S0217595923500203BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940464"},{"key":"S0217595923500203BIB011","volume-title":"Numerical Optimization","author":"Nocedal J","year":"2006","edition":"2"},{"key":"S0217595923500203BIB012","volume-title":"Concise Numerical Mathematics, Graduate Studies in Mathematics","volume":"57","author":"Plato R","year":"2003"},{"key":"S0217595923500203BIB013","first-page":"35","volume":"16","author":"Polak B","year":"1969","journal-title":"Revue Francaise D\u2019informatique et de Recherche Op\u00e9rationnelle"},{"key":"S0217595923500203BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(69)90035-4"},{"key":"S0217595923500203BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21738-3"},{"key":"S0217595923500203BIB016","doi-asserted-by":"publisher","DOI":"10.1137\/1011036"},{"key":"S0217595923500203BIB017","doi-asserted-by":"publisher","DOI":"10.1137\/1013035"},{"key":"S0217595923500203BIB018","doi-asserted-by":"publisher","DOI":"10.1080\/10556780701661344"},{"key":"S0217595923500203BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.05.032"},{"key":"S0217595923500203BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0028-z"},{"key":"S0217595923500203BIB021","first-page":"37","volume-title":"Integer and Nonlinear Programming","author":"Zoutendijk G","year":"1970"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595923500203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T03:44:34Z","timestamp":1712547874000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595923500203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,12]]},"references-count":21,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["10.1142\/S0217595923500203"],"URL":"https:\/\/doi.org\/10.1142\/s0217595923500203","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"type":"print","value":"0217-5959"},{"type":"electronic","value":"1793-7019"}],"subject":[],"published":{"date-parts":[[2023,6,12]]},"article-number":"2350020"}}