{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,31]],"date-time":"2024-08-31T00:17:03Z","timestamp":1725063423995},"reference-count":30,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems.\nIn this paper, a new hybrid conjugate gradient (CG) method is presented and analyzed for solving unconstrained optimization problems, where the parameter <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\u03b2<\/m:mi>\n                              <m:mi>k<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2007_ineq_0001.png\"\/>\n                        <jats:tex-math>\\beta_{k}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is a convex combination of <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msubsup>\n                              <m:mi>\u03b2<\/m:mi>\n                              <m:mi>k<\/m:mi>\n                              <m:mi>WYL<\/m:mi>\n                           <\/m:msubsup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2007_ineq_0002.png\"\/>\n                        <jats:tex-math>\\beta_{k}^{\\mathrm{WYL}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msubsup>\n                              <m:mi>\u03b2<\/m:mi>\n                              <m:mi>k<\/m:mi>\n                              <m:mi>CD<\/m:mi>\n                           <\/m:msubsup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2007_ineq_0003.png\"\/>\n                        <jats:tex-math>\\beta_{k}^{\\mathrm{CD}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.\nUnder the strong Wolfe line search, the new method possesses the sufficient descent condition and the global convergence properties.\nThe preliminary numerical results show the efficiency of our method in comparison with other CG methods.\nFurthermore, the proposed algorithm HWYLCD was extended to solve the problem of a mode function.<\/jats:p>","DOI":"10.1515\/mcma-2024-2007","type":"journal-article","created":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T01:11:59Z","timestamp":1718932319000},"page":"225-234","source":"Crossref","is-referenced-by-count":1,"title":["Another hybrid conjugate gradient method as a convex combination of WYL and CD methods"],"prefix":"10.1515","volume":"30","author":[{"given":"Imane","family":"Guefassa","sequence":"first","affiliation":[{"name":"Laboratory Informatics and Mathematics (LIM) , Mohamed Cherif Messaadia University , Souk Ahras , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yacine","family":"Chaib","sequence":"additional","affiliation":[{"name":"Laboratory Informatics and Mathematics (LIM) , Mohamed Cherif Messaadia University , Souk Ahras , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tahar","family":"Bechouat","sequence":"additional","affiliation":[{"name":"Laboratory Informatics and Mathematics (LIM) , Mohamed Cherif Messaadia University , Souk Ahras , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,6,21]]},"reference":[{"key":"2024083008370660108_j_mcma-2024-2007_ref_001","unstructured":"N. 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Andrei,\nNew hybrid conjugate gradient algorithms for unconstrained optimization,\nEncyclopedia Optimization,\nSpringer, Boston (2009), 2560\u20132571.","DOI":"10.1007\/978-0-387-74759-0_441"},{"key":"2024083008370660108_j_mcma-2024-2007_ref_005","doi-asserted-by":"crossref","unstructured":"I. Bongartz, A. R. Conn, N. Gould and P. L. Toint,\nConstrained and unconstrained testing environment,\nACM Trans. Math. Software (TOMS) 21 (1995), 123\u2013160.","DOI":"10.1145\/200979.201043"},{"key":"2024083008370660108_j_mcma-2024-2007_ref_006","doi-asserted-by":"crossref","unstructured":"Y. H. Dai and Y. Yuan,\nA nonlinear conjugate gradient method with a strong global convergence property,\nSIAM J. Optim. 10 (1999), no. 1, 177\u2013182.","DOI":"10.1137\/S1052623497318992"},{"key":"2024083008370660108_j_mcma-2024-2007_ref_007","doi-asserted-by":"crossref","unstructured":"Y. H. Dai and Y. Yuan,\nAn efficient hybrid conjugate gradient method for unconstrained optimization,\nAnn. Oper. 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