{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T07:11:13Z","timestamp":1763968273456},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T00:00:00Z","timestamp":1521158400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s11590-018-1247-9","type":"journal-article","created":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T05:40:46Z","timestamp":1521178846000},"page":"617-632","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Gradient method with multiple damping for large-scale unconstrained optimization"],"prefix":"10.1007","volume":"13","author":[{"given":"Hong Seng","family":"Sim","sequence":"first","affiliation":[]},{"given":"Wah June","family":"Leong","sequence":"additional","affiliation":[]},{"given":"Chuei Yee","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,16]]},"reference":[{"key":"1247_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01831719","volume":"11","author":"H Akaike","year":"1959","unstructured":"Akaike, H.: On a successive transformation of probability distribution and its applications to analysis of the optimum gradient method. Ann. Inst. Stat. Math. Tokyo 11, 1\u201317 (1959)","journal-title":"Ann. Inst. Stat. Math. Tokyo"},{"key":"1247_CR2","first-page":"147","volume":"10","author":"N Andrei","year":"2008","unstructured":"Andrei, N.: An unconstrained optimization test functions collection. J. Adv. Model Optim. 10, 147\u2013161 (2008)","journal-title":"J. Adv. Model Optim."},{"key":"1247_CR3","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/s10851-015-0591-y","volume":"54","author":"L Antonelli","year":"2016","unstructured":"Antonelli, L., De Simone, V., di Serafino, D.: On the application of the spectral projected gradient method in image segmentation. J. Math. Imaging Vis. 54, 106\u2013116 (2016)","journal-title":"J. Math. Imaging Vis."},{"key":"1247_CR4","doi-asserted-by":"publisher","first-page":"015002","DOI":"10.1088\/0266-5611\/25\/1\/015002","volume":"25","author":"S Bonettini","year":"2009","unstructured":"Bonettini, S., Zanella, R., Zanni, L.: A scaled gradient projection method for constrained image deblurring. Inverse Probl. 25, 015002 (2009)","journal-title":"Inverse Probl."},{"key":"1247_CR5","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1145\/200979.201043","volume":"21","author":"I Bongartz","year":"1995","unstructured":"Bongartz, I., Conn, A.R., Gould, N.I.M., Toint, PhL: CUTE: constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 123\u2013160 (1995)","journal-title":"ACM Trans. Math. Softw."},{"key":"1247_CR6","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1137\/0726042","volume":"26","author":"RH Byrd","year":"1989","unstructured":"Byrd, R.H., Nocedal, J.: A tool for the analysis of quasi-Newton methods with application to unconstrained minimization. SIAM J. Numer. Anal. 26, 727\u2013739 (1989)","journal-title":"SIAM J. Numer. Anal."},{"key":"1247_CR7","first-page":"46","volume":"25","author":"A Cauchy","year":"1847","unstructured":"Cauchy, A.: M\u00e9thode g\u00e9n\u00e9rale pour la r\u00e9solution des syst\u00e8ms d\u2019 \u00e9quations simultan\u00e9es. Comp. Rend. Sci. Paris 25, 46\u201389 (1847)","journal-title":"Comp. Rend. Sci. Paris"},{"key":"1247_CR8","doi-asserted-by":"publisher","first-page":"181","DOI":"10.3934\/jimo.2005.1.181","volume":"1","author":"Y Dai","year":"2005","unstructured":"Dai, Y., Yuan, Y.: Analysis of monotone gradient methods. J. Ind. Manag. Optim. 1, 181\u2013192 (2005)","journal-title":"J. Ind. Manag. Optim."},{"key":"1247_CR9","doi-asserted-by":"publisher","first-page":"1416","DOI":"10.1093\/imanum\/drs056","volume":"33","author":"R Asmundis De","year":"2013","unstructured":"De Asmundis, R., di Serafino, D., Riccio, F., Toraldo, G.: On spectral properties of steepest descent methods. IMA J. Numer. Anal. 33, 1416\u20131435 (2013)","journal-title":"IMA J. Numer. Anal."},{"key":"1247_CR10","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/s10589-014-9669-5","volume":"59","author":"R Asmundis De","year":"2014","unstructured":"De Asmundis, R., di Serafino, D., Hager, W., Toraldo, G., Zhang, H.: An efficient gradient method using the Yuan steplength. Comput. Optim. Appl. 59, 541\u2013563 (2014)","journal-title":"Comput. Optim. Appl."},{"key":"1247_CR11","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.cam.2016.01.007","volume":"302","author":"R Asmundis De","year":"2016","unstructured":"De Asmundis, R., di Serafino, D., Landi, G.: On the regularizing behavior of the SDA and SDC gradient methods in the solution of linear ill-posed problems. J. Comput. Appl. Math. 302, 81\u201393 (2016)","journal-title":"J. Comput. Appl. Math."},{"key":"1247_CR12","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.amc.2017.07.037","volume":"318","author":"D Serafino di","year":"2018","unstructured":"di Serafino, D., Ruggiero, V., Toraldo, G., Zanni, L.: On the steplength selection in gradient methods for unconstrained optimization. Appl. Math. Comput. 318, 176\u2013195 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1247_CR13","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"E Dolan","year":"2002","unstructured":"Dolan, E., Mor\u00e9, J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"1247_CR14","volume-title":"Practical Methods of Optimization Vol 1: Unconstrained Optimization","author":"R Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization Vol 1: Unconstrained Optimization. Wiley, New York (1987)"},{"key":"1247_CR15","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/s10107-011-0479-6","volume":"135","author":"R Fletcher","year":"2012","unstructured":"Fletcher, R.: A limited memory steepest descent method. Math. Program. 135, 413\u2013436 (2012)","journal-title":"Math. Program."},{"key":"1247_CR16","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1093\/comjnl\/7.2.149","volume":"7","author":"R Fletcher","year":"1964","unstructured":"Fletcher, R., Reeves, C.: Function minimization by conjugate gradients. Comput. J. 7, 149\u2013154 (1964)","journal-title":"Comput. J."},{"key":"1247_CR17","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1002\/jcc.540140115","volume":"14","author":"W Glunt","year":"1993","unstructured":"Glunt, W., Hayden, T.L., Raydan, M.: Molecular conformations from distance matrices. J. Comput. Chem. 14, 114\u2013120 (1993)","journal-title":"J. Comput. Chem."},{"key":"1247_CR18","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s10589-015-9775-z","volume":"63","author":"C Gonzaga","year":"2016","unstructured":"Gonzaga, C., Schneider, R.M.: On the steepest descent algorithm for quadratic functions. Comput. Optim. Appl. 63, 523\u2013542 (2016)","journal-title":"Comput. Optim. Appl."},{"issue":"19","key":"1247_CR19","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L Grippo","year":"1986","unstructured":"Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search techniques for Newton\u2019s method. SIAM J. Numer. Anal. 23(19), 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1247_CR20","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/030601880","volume":"16","author":"WW Hager","year":"2005","unstructured":"Hager, W.W., Zhang, H.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16(1), 170\u2013192 (2005)","journal-title":"SIAM J. Optim."},{"key":"1247_CR21","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718898","volume-title":"Solving Nonlinear Equations with Newton\u2019s Method Number 1 in Fundamental Algorithms for Numerical Calculations","author":"CT Kelley","year":"2003","unstructured":"Kelley, C.T.: Solving Nonlinear Equations with Newton\u2019s Method Number 1 in Fundamental Algorithms for Numerical Calculations. SIAM, Philadelphia (2003)"},{"key":"1247_CR22","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF00940464","volume":"69","author":"Y Liu","year":"1991","unstructured":"Liu, Y., Storey, C.: Efficient generalized conjugate gradient algorithms, part 1: theory. J. Optim. Theory Appl. 69, 129\u2013137 (1991)","journal-title":"J. Optim. Theory Appl."},{"key":"1247_CR23","volume-title":"Linear and Nonlinear Programming","author":"DG Luenberger","year":"1984","unstructured":"Luenberger, D.G.: Linear and Nonlinear Programming, 2nd edn. Addison-Wesley, Reading (1984)","edition":"2"},{"key":"1247_CR24","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1023\/A:1020181927999","volume":"30","author":"F Luengo","year":"2002","unstructured":"Luengo, F., Raydan, M., Glunt, W., HaydenPreconditioned, T.L.: Spectral gradient method. Numer. Algorithms 30, 241\u2013258 (2002)","journal-title":"Numer. Algorithms"},{"key":"1247_CR25","first-page":"35","volume":"16","author":"E Polak","year":"1969","unstructured":"Polak, E., Ribiere, G.: Note sur la convergence de directions conjugees, Rev. Francaise Informat. Recherche Opertionelle 3e Annee 16, 35\u201343 (1969)","journal-title":"Recherche Opertionelle 3e Annee"},{"key":"1247_CR26","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/0041-5553(69)90035-4","volume":"9","author":"BT Polyak","year":"1969","unstructured":"Polyak, B.T.: The conjugate gradient method in extreme problems. USSR Comput. Math. Math. Phys. 9, 94\u2013112 (1969)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"1247_CR27","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1137\/S1052623494266365","volume":"7","author":"M Raydan","year":"1997","unstructured":"Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained optimization. SIAM J. Optim. 7, 26\u201333 (1997)","journal-title":"SIAM J. Optim."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-018-1247-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-018-1247-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-018-1247-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T10:18:53Z","timestamp":1603966733000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-018-1247-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,16]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["1247"],"URL":"https:\/\/doi.org\/10.1007\/s11590-018-1247-9","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,16]]},"assertion":[{"value":"2 March 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}