{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T04:53:27Z","timestamp":1767588807898,"version":"3.41.2"},"reference-count":52,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100003968","name":"Iran National Science Foundation","doi-asserted-by":"crossref","award":["4000309"],"award-info":[{"award-number":["4000309"]}],"id":[{"id":"10.13039\/501100003968","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p> In an effort to make modification on the classical Polak\u2013Ribi\u00e8re\u2013Polyak method, Wei et al. suggested an efficient nonlinear conjugate gradient method which possesses the sufficient descent property when the line search fulfills the strong Wolfe conditions (by restricting the line search parameters). Here, we develop a three-term extension of the method which satisfies the sufficient descent condition independent of the line search. Also, under a backtracking Armijo-type line search, we establish global convergence of the method without convexity assumption. Using a scalar approximation of the Hessian of the objective function, we suggest an acceleration scheme that can be used in the iterative line search methods of unconstrained optimization. At last, practical merits of the proposed method are investigated by numerical experiments on a set of CUTEr test functions as well as the well-known image restoration problem. The results show numerical efficiency of the method. <\/jats:p>","DOI":"10.1142\/s0217595922500476","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T04:52:47Z","timestamp":1670993567000},"source":"Crossref","is-referenced-by-count":1,"title":["An Accelerated Three-Term Extension of a Descent Nonlinear Conjugate Gradient Method"],"prefix":"10.1142","volume":"40","author":[{"given":"Zohre","family":"Aminifard","sequence":"first","affiliation":[{"name":"Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran"}]},{"given":"Saman","family":"Babaie-Kafaki","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran"}]},{"given":"Nasrin","family":"Mirhoseini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran"}]}],"member":"219","published-online":{"date-parts":[[2023,3,9]]},"reference":[{"key":"S0217595922500476BIB001","doi-asserted-by":"crossref","first-page":"100069","DOI":"10.1016\/j.rinam.2019.100069","volume":"4","author":"Abubakar AB","year":"2019","journal-title":"Results in Applied Mathematics"},{"key":"S0217595922500476BIB002","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10288-018-0387-1","volume":"17","author":"Aminifard Z","year":"2019","journal-title":"4OR"},{"issue":"1","key":"S0217595922500476BIB003","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11075-006-9023-9","volume":"42","author":"Andrei N","year":"2006","journal-title":"Numerical Algorithms"},{"issue":"2","key":"S0217595922500476BIB004","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s11075-007-9152-9","volume":"47","author":"Andrei N","year":"2008","journal-title":"Numerical Algorithms"},{"issue":"3","key":"S0217595922500476BIB005","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.ejor.2009.11.030","volume":"204","author":"Andrei N","year":"2010","journal-title":"European Journal of Operational Research"},{"key":"S0217595922500476BIB006","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/j.apnum.2019.05.012","volume":"145","author":"Awwal AM","year":"2019","journal-title":"Applied Numerical Mathematics"},{"issue":"12","key":"S0217595922500476BIB007","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.1016\/j.camwa.2014.09.019","volume":"68","author":"Babaie-Kafaki S","year":"2014","journal-title":"Computers and Mathematics with Applications"},{"issue":"3","key":"S0217595922500476BIB008","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1080\/10556788.2013.833199","volume":"29","author":"Babaie-Kafaki S","year":"2014","journal-title":"Optimization Methods and Software"},{"issue":"3","key":"S0217595922500476BIB009","doi-asserted-by":"crossref","first-page":"465","DOI":"10.36045\/bbms\/1407765884","volume":"21","author":"Babaie-Kafaki S","year":"2014","journal-title":"Bulletin of the Belgian Mathematical Society \u2014 Simon Stevin"},{"key":"S0217595922500476BIB010","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1007\/s11075-017-0406-x","volume":"78","author":"Babaie-Kafaki S","year":"2018","journal-title":"Numerical Algorithms"},{"issue":"1","key":"S0217595922500476BIB011","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"Barzilai J","year":"1988","journal-title":"IMA Journal of Numerical Analysis"},{"issue":"11","key":"S0217595922500476BIB012","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1007\/s11075-019-00709-7","volume":"83","author":"Bojari S","year":"2020","journal-title":"Numerical Algorithms"},{"key":"S0217595922500476BIB013","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/s11063-018-9948-8","volume":"50","author":"Borhani M","year":"2019","journal-title":"Neural Processing Letters"},{"key":"S0217595922500476BIB014","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.apnum.2019.12.002","volume":"152","author":"Cao J","year":"2020","journal-title":"Applied Numerical Mathematics"},{"issue":"2","key":"S0217595922500476BIB015","first-page":"348","volume":"10","author":"Dai YH","year":"1999","journal-title":"SIAM Journal on Optimization"},{"key":"S0217595922500476BIB016","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1007\/s42452-019-1670-2","volume":"1","author":"de Leeuw den Bouter ML","year":"2019","journal-title":"SN Applied Sciences"},{"key":"S0217595922500476BIB017","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11075-018-0591-2","volume":"82","author":"Dehghani R","year":"2019","journal-title":"Numerical Algorithms"},{"issue":"2","key":"S0217595922500476BIB018","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"Dolan ED","year":"2002","journal-title":"Mathematical Programming"},{"issue":"5","key":"S0217595922500476BIB019","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1080\/02331934.2017.1295242","volume":"66","author":"Dong XL","year":"2017","journal-title":"Optimization"},{"issue":"1","key":"S0217595922500476BIB020","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10092-018-0296-x","volume":"56","author":"Esmaeili H","year":"2019","journal-title":"Calcolo"},{"key":"S0217595922500476BIB021","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.cpc.2018.09.004","volume":"235","author":"Exl L","year":"2019","journal-title":"Computer Physics Communications"},{"key":"S0217595922500476BIB022","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1007\/s10957-019-01527-6","volume":"182","author":"Faramarzi P","year":"2019","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"S0217595922500476BIB023","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1137\/0802003","volume":"2","author":"Gilbert JC","year":"1992","journal-title":"SIAM Journal on Optimization"},{"issue":"4","key":"S0217595922500476BIB024","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1145\/962437.962439","volume":"29","author":"Gould NIM","year":"2003","journal-title":"ACM Transactions on Mathematical Software"},{"issue":"1","key":"S0217595922500476BIB025","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1145\/1132973.1132979","volume":"32","author":"Hager WW","year":"2006","journal-title":"ACM Transactions on Mathematical Software"},{"issue":"1","key":"S0217595922500476BIB026","first-page":"35","volume":"2","author":"Hager WW","year":"2006","journal-title":"Pacific Journal of Optimization"},{"issue":"12","key":"S0217595922500476BIB027","doi-asserted-by":"crossref","first-page":"6252","DOI":"10.1109\/TNNLS.2018.2827778","volume":"29","author":"Heravi AR","year":"2018","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"issue":"6","key":"S0217595922500476BIB028","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"Hestenes MR","year":"1952","journal-title":"Journal of Research of the National Bureau of Standards"},{"key":"S0217595922500476BIB029","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1016\/j.amc.2006.12.006","volume":"189","author":"Huang H","year":"2007","journal-title":"Applied Mathematics and Computation"},{"key":"S0217595922500476BIB030","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1016\/j.apm.2014.08.008","volume":"39","author":"Jian JB","year":"2015","journal-title":"Applied Mathematical Modelling"},{"key":"S0217595922500476BIB031","first-page":"103","volume":"34","author":"Jiang XZ","year":"2012","journal-title":"Mathematica Numerica Sinica"},{"key":"S0217595922500476BIB032","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1007\/s11063-017-9737-9","volume":"48","author":"Li W","year":"2018","journal-title":"Neural Processing Letters"},{"key":"S0217595922500476BIB033","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.camwa.2016.11.017","volume":"73","author":"Li X","year":"2017","journal-title":"Computers and Mathematics with Applications"},{"key":"S0217595922500476BIB034","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s11053-019-09509-1","volume":"29","author":"Lin N","year":"2020","journal-title":"Natural Resources Research"},{"key":"S0217595922500476BIB035","doi-asserted-by":"crossref","first-page":"107412","DOI":"10.1016\/j.sigpro.2019.107412","volume":"169","author":"Lin J","year":"2020","journal-title":"Signal Processing"},{"key":"S0217595922500476BIB036","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1007\/s13351-018-8053-2","volume":"32","author":"Liu Y","year":"2018","journal-title":"Journal of Meteorological Research"},{"issue":"1","key":"S0217595922500476BIB037","first-page":"21","volume":"8","author":"Nezhadhosein S","year":"2020","journal-title":"Journal of Mathematical Modeling"},{"volume-title":"Numerical Optimization","year":"2006","author":"Nocedal J","key":"S0217595922500476BIB038"},{"issue":"1","key":"S0217595922500476BIB039","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/BF01580654","volume":"10","author":"Oren SS","year":"1976","journal-title":"Mathematical Programming"},{"issue":"3","key":"S0217595922500476BIB040","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s10957-011-9960-x","volume":"153","author":"Sugiki K","year":"2012","journal-title":"Journal of Optimization Theory and Applications"},{"volume-title":"Optimization Theory and Methods: Nonlinear Programming","year":"2006","author":"Sun W","key":"S0217595922500476BIB041"},{"key":"S0217595922500476BIB042","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1007\/s11760-018-1300-2","volume":"12","author":"Wan Z","year":"2018","journal-title":"Signal, Image and Video Processing"},{"key":"S0217595922500476BIB043","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s10092-015-0140-5","volume":"53","author":"Wang XY","year":"2016","journal-title":"Calcolo"},{"key":"S0217595922500476BIB044","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/j.amc.2006.05.150","volume":"183","author":"Wei ZX","year":"2006","journal-title":"Applied Mathematics and Computation"},{"issue":"5","key":"S0217595922500476BIB045","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.aml.2010.01.010","volume":"23","author":"Yu G","year":"2010","journal-title":"Applied Mathematics Letters"},{"issue":"1","key":"S0217595922500476BIB046","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1186\/s13660-019-2192-6","volume":"2019","author":"Yuan G","year":"2019","journal-title":"Journal of Inequalities and Applications"},{"key":"S0217595922500476BIB047","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.apnum.2019.08.022","volume":"147","author":"Yuan G","year":"2020","journal-title":"Applied Numerical Mathematics"},{"key":"S0217595922500476BIB048","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2020.01.019","volume":"152","author":"Yuan G","year":"2020","journal-title":"Applied Numerical Mathematics"},{"issue":"1","key":"S0217595922500476BIB049","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s10957-015-0781-1","volume":"168","author":"Yuan G","year":"2016","journal-title":"Journal of Optimization Theory and Applications"},{"key":"S0217595922500476BIB050","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.cam.2018.10.057","volume":"362","author":"Yuan G","year":"2019","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"4","key":"S0217595922500476BIB051","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1093\/imanum\/drl016","volume":"26","author":"Zhang L","year":"2006","journal-title":"IMA Journal of Numerical Analysis"},{"issue":"4","key":"S0217595922500476BIB052","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1080\/10556780701223293","volume":"22","author":"Zhang L","year":"2007","journal-title":"Optimization Methods and Software"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595922500476","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T07:28:12Z","timestamp":1686814092000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595922500476"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,9]]},"references-count":52,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["10.1142\/S0217595922500476"],"URL":"https:\/\/doi.org\/10.1142\/s0217595922500476","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"type":"print","value":"0217-5959"},{"type":"electronic","value":"1793-7019"}],"subject":[],"published":{"date-parts":[[2023,3,9]]},"article-number":"2250047"}}