{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T10:26:29Z","timestamp":1750760789453,"version":"3.37.3"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T00:00:00Z","timestamp":1587427200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T00:00:00Z","timestamp":1587427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100015515","name":"kementerian pendidikan malaysia","doi-asserted-by":"crossref","award":["FRGS\/1\/2019\/STG06\/UPM\/02\/14"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UPM\/02\/14"]}],"id":[{"id":"10.13039\/501100015515","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s11075-020-00930-9","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T15:10:26Z","timestamp":1587481826000},"page":"1225-1241","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Diagonal quasi-Newton methods via least change updating principle with weighted Frobenius norm"],"prefix":"10.1007","volume":"86","author":[{"given":"Wah June","family":"Leong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sharareh","family":"Enshaei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sie Long","family":"Kek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,4,21]]},"reference":[{"key":"930_CR1","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":"930_CR2","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, P. h. L.: CUTE: Constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 123\u2013160 (1995)","journal-title":"ACM Trans. Math. Softw."},{"key":"930_CR3","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1093\/imamat\/12.3.223","volume":"12","author":"CG Broyden","year":"1973","unstructured":"Broyden, C.G., Dennis, J.E., Mor\u00e9, J.J.: On the local and superlinear convergence of quasi-Newton methods. J. Inst. Math. Appl. 12, 223\u2013246 (1973)","journal-title":"J. Inst. Math. Appl."},{"key":"930_CR4","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1137\/0724077","volume":"24","author":"RH Byrd","year":"1987","unstructured":"Byrd, R.H., Nocedal, J., Yuan, Y.: Global convergence of a class of quasi-Newton methods on convex problems. SIAM J. Numer. Anal. 24, 1171\u20131190 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"930_CR5","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1137\/S1052623497318992","volume":"10","author":"Y Dai","year":"1999","unstructured":"Dai, Y., Yuan, Y.: A nonlinear conjugate gradient method with a strong convergence property. SIAM J. Optim. 10, 177\u2013182 (1999)","journal-title":"SIAM J. Optim."},{"key":"930_CR6","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1090\/S0025-5718-1974-0343581-1","volume":"28","author":"JE Dennis","year":"1974","unstructured":"Dennis, J.E., Mor\u00e9, J.J.: A characterization of superlinear convergence and its application to quasi-Newton methods. Math. Comp. 28, 549\u2013560 (1974)","journal-title":"Math. Comp."},{"key":"930_CR7","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1137\/0730067","volume":"30","author":"JE Dennis","year":"1993","unstructured":"Dennis, J.E., Wolkowicz, H.: Sizing and least change secant methods. SIAM J. Numer. Anal. 30, 1291\u20131313 (1993)","journal-title":"SIAM J. Numer. Anal."},{"key":"930_CR8","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":"930_CR9","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":"930_CR10","first-page":"1","volume":"24","author":"J Greenstadt","year":"1970","unstructured":"Greenstadt, J.: Variations on variable-metric methods. Math. Comp. 24, 1\u201322 (1970)","journal-title":"Math. Comp."},{"key":"930_CR11","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/030601880","volume":"16","author":"W Hager","year":"2005","unstructured":"Hager, W., Zhang, H.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16, 170\u2013192 (2005)","journal-title":"SIAM J. Optim."},{"key":"930_CR12","volume-title":"Inequalities","author":"GH Hardy","year":"1988","unstructured":"Hardy, G.H., Littlewood, J.E., P\u00f2lya, G.: Inequalities, S2. Cambridge University Press, Cambridge (1988)","edition":"S2"},{"key":"930_CR13","doi-asserted-by":"publisher","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"MR Hestenes","year":"1952","unstructured":"Hestenes, M.R., Stiefel, E.L.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. B 49, 409\u2013432 (1952)","journal-title":"J. Res. Natl. Bur. Stand. B"},{"key":"930_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/0803001","volume":"3","author":"H Khalfan","year":"1993","unstructured":"Khalfan, H., Byrd, R.H., Schnabel, R.B.: A theoretical and experimental study of the symmetric rank one update. SIAM J. Optim. 3, 1\u201324 (1993)","journal-title":"SIAM J. Optim."},{"key":"930_CR15","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.jcp.2019.06.049","volume":"396","author":"J Li","year":"2019","unstructured":"Li, J., Ying, J., Lu, B.: A flux-jump preserved gradient recovery technique for accurately predicting the electrostatics field of an immersed biomolecules. J. Comput. Phys. 396, 193\u2013208 (2019)","journal-title":"J. Comput. Phys."},{"key":"930_CR16","first-page":"11","volume":"6","author":"JL Nazareth","year":"1995","unstructured":"Nazareth, J.L.: If quasi-Newton then why not quasi-Cauchy? SIAG\/OPT Views-and-News 6, 11\u201314 (1995)","journal-title":"SIAG\/OPT Views-and-News"},{"key":"930_CR17","unstructured":"Nazareth, J.L.: The quasi-Cauchy method: a stepping stone to derivative-free algorithms, Technical Report No. 95-3, Department of Pure and Applied Mathematics, Washington State University WA (1995)"},{"key":"930_CR18","first-page":"845","volume":"20","author":"SS Oren","year":"1974","unstructured":"Oren, S.S., Luenberger, D.G.: Self-scaling variable metric (SSVM) algorithms, I: Criteria and sufficient conditions for scaling a class of algorithms. Manag. Sc. 20, 845\u2013862 (1974)","journal-title":"Manag. Sc."},{"key":"930_CR19","first-page":"35","volume":"16","author":"B Polak","year":"1969","unstructured":"Polak, B., Ribi\u00e8re, G.: Note surla convergence des m\u00e9thodes de directions conjugu\u00e9es. Rev. Francaise Infomat Recherche Operatonelle, 3e Ann\u00e9e 16, 35\u201343 (1969)","journal-title":"Rev. Francaise Infomat Recherche Operatonelle, 3e Ann\u00e9e"},{"key":"930_CR20","doi-asserted-by":"crossref","unstructured":"Powell, M.J.D.: A new algorithm for unconstrained optimization. In: Rosen, J. B., Mangasarian, O. L., Ritter, K (eds.) Nonlinear Programming. Academic Press, New York (1970)","DOI":"10.1016\/B978-0-12-597050-1.50006-3"},{"key":"930_CR21","unstructured":"Powell, M.J.D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: Cottle, R.W., Lemke, C.E (eds.) Nonlinear Programming, SIAM-AMS Proceedings, pp 53\u201372. SIAM, Philadelphia (1976)"},{"key":"930_CR22","first-page":"95","volume":"13","author":"Y Yuan","year":"1995","unstructured":"Yuan, Y., Byrd, R.H.: Non-quasi-Newton updates for unconstrained optimization. J. Comput. Math. 13, 95\u2013107 (1995)","journal-title":"J. Comput. Math."},{"key":"930_CR23","doi-asserted-by":"publisher","first-page":"1192","DOI":"10.1137\/S1052623498331793","volume":"9","author":"M Zhu","year":"1999","unstructured":"Zhu, M., Nazareth, J.L., Wolkowicz, H.: The quasi-Cauchy relation and diagonal updating. SIAM J. Optim. 9, 1192\u20131204 (1999)","journal-title":"SIAM J. Optim."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-00930-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-020-00930-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-020-00930-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T00:37:48Z","timestamp":1618965468000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-020-00930-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,21]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["930"],"URL":"https:\/\/doi.org\/10.1007\/s11075-020-00930-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2020,4,21]]},"assertion":[{"value":"25 January 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}