{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:41:41Z","timestamp":1760402501003,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,5]],"date-time":"2022-01-05T00:00:00Z","timestamp":1641340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a three-parameter subspace conjugate gradient method is proposed for solving large-scale unconstrained optimization problems. By minimizing the quadratic approximate model of the objective function on a new special three-dimensional subspace, the embedded parameters are determined and the corresponding algorithm is obtained. The global convergence result of a given method for general nonlinear functions is established under mild assumptions. In numerical experiments, the proposed algorithm is compared with SMCG_NLS and SMCG_Conic, which shows that the given algorithm is robust and efficient.<\/jats:p>","DOI":"10.3390\/sym14010080","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"80","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Class of Three-Dimensional Subspace Conjugate Gradient Algorithms for Unconstrained Optimization"],"prefix":"10.3390","volume":"14","author":[{"given":"Jun","family":"Huo","sequence":"first","affiliation":[{"name":"Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, China"}]},{"given":"Jielan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning 530004, China"}]},{"given":"Guoxin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning 530004, China"}]},{"given":"Shengwei","family":"Yao","sequence":"additional","affiliation":[{"name":"Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, China"},{"name":"Guangxi Key Laboratory Cultivation Base of Cross-Border E-Commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning 530007, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","article-title":"Methods of conjugate gradients for solving linear systems","volume":"49","author":"Hestenes","year":"1952","journal-title":"J. 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