{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T18:49:09Z","timestamp":1762022949308,"version":"build-2065373602"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T00:00:00Z","timestamp":1587340800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T00:00:00Z","timestamp":1587340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s12190-020-01350-7","type":"journal-article","created":{"date-parts":[[2020,4,20]],"date-time":"2020-04-20T15:04:29Z","timestamp":1587395069000},"page":"179-194","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Two nonmonotone trust region algorithms based on an improved Newton method"],"prefix":"10.1007","volume":"64","author":[{"given":"T. Dehghan","family":"Niri","sequence":"first","affiliation":[]},{"given":"M.","family":"Heydari","sequence":"additional","affiliation":[]},{"given":"M. M.","family":"Hosseini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,20]]},"reference":[{"key":"1350_CR1","first-page":"291","volume":"67","author":"R Abdullah","year":"1998","unstructured":"Abdullah, R., Evans, D.J.: Communication analysis of the PIE and QIF algorithms on distributed memory architectures. Int. J. Comput. Marin. 67, 291\u2013313 (1998)","journal-title":"Int. J. Comput. Marin."},{"key":"1350_CR2","unstructured":"Andrei, N.: Test functions for unconstrained optimization, 8\u201310, Averescu Avenue, Sector 1, Bucharest. Romania, Academy of Romanian Scientists (2004)"},{"key":"1350_CR3","first-page":"147","volume":"10","author":"N Andrei","year":"2008","unstructured":"Andrei, N.: An unconstrained optimization test functions collection. Adv. Model. Optim. 10, 147\u2013161 (2008)","journal-title":"Adv. Model. Optim."},{"key":"1350_CR4","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.amc.2008.04.046","volume":"203","author":"S Chandra Sekhara Rao","year":"2008","unstructured":"Chandra Sekhara Rao, S., Sarita: A symmetric linear system solver. Appl. Math. Comput. 203, 368\u2013379 (2008)","journal-title":"Appl. Math. Comput."},{"key":"1350_CR5","first-page":"69","volume":"7","author":"T Dehghan Niri","year":"2019","unstructured":"Dehghan Niri, T., Hosseini, M.M., Heydari, M.: An efficient improvement of the newton method for solving nonconvex optimization problems. Comput. Methods Differ. Equ. 7, 69\u201385 (2019)","journal-title":"Comput. Methods Differ. Equ."},{"key":"1350_CR6","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s12190-019-01272-z","volume":"62","author":"T Dehghan Niri","year":"2020","unstructured":"Dehghan Niri, T., Shahzadeh Fazeli, S.A., Heydari, M.: A two-step improved Newton method to solve convex unconstrained optimization problems. J. Appl. Math. Comput. 62, 37\u201353 (2020)","journal-title":"J. Appl. Math. Comput."},{"key":"1350_CR7","first-page":"115","volume":"12","author":"T Dehghan Niri","year":"2018","unstructured":"Dehghan Niri, T., Heydari, M., Hosseini, M.M.: A new modified trust region algorithm for solving unconstrained optimization problems. J. Math. Ext. 12, 115\u2013135 (2018)","journal-title":"J. Math. Ext."},{"key":"1350_CR8","doi-asserted-by":"publisher","unstructured":"Dehghan Niri, T., Heydari, M., Hosseini, M.M.: Correction of trust region method with a new modified Newton method. Int. J. Comput. Math. https:\/\/doi.org\/10.1080\/00207160.2019.1607844 (2019)","DOI":"10.1080\/00207160.2019.1607844"},{"key":"1350_CR9","doi-asserted-by":"publisher","unstructured":"Dehghan Niri, T., Shahzadeh Fazeli, S.A., Hosseini, M.M.: Using a new regularized factorization method for unconstrained optimization problems, International journal of numerical modelling electronic networks devices and fields. https:\/\/doi.org\/10.1002\/jnm.2580 (2019)","DOI":"10.1002\/jnm.2580"},{"key":"1350_CR10","doi-asserted-by":"crossref","unstructured":"Dennis, J.E., Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equation (1996)","DOI":"10.1137\/1.9781611971200"},{"key":"1350_CR11","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., More, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"1350_CR12","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1080\/00207169908804852","volume":"72","author":"DJ Evans","year":"1999","unstructured":"Evans, D.J.: The Cholesky Q.I.F. algorithm for solving symmetric linear systems. Int. J. Comput. Math. 72, 283\u2013288 (1999)","journal-title":"Int. J. Comput. Math."},{"key":"1350_CR13","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s10589-005-3078-8","volume":"34","author":"JY Fan","year":"2006","unstructured":"Fan, J.Y.: Convergence rate of the trust region method for nonlinear equations under local error bound condition. Comput. Optim. Appl. 34, 215\u2013227 (2006)","journal-title":"Comput. Optim. Appl."},{"key":"1350_CR14","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s00607-004-0083-1","volume":"74","author":"JY Fan","year":"2005","unstructured":"Fan, J.Y., Yuan, Y.X.: On the quadratic convergence of the Levenberg\u2013Marquardt method without nonsingularity assumption. Computing 74, 23\u201339 (2005)","journal-title":"Computing"},{"key":"1350_CR15","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.amc.2008.10.056","volume":"207","author":"JY Fan","year":"2009","unstructured":"Fan, J.Y., Pan, J.Y.: A note on the Levenberge\u2013Marquardt parameter. Appl. Math. Comput. 207, 351\u2013359 (2009)","journal-title":"Appl. Math. Comput."},{"key":"1350_CR16","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 technique for Newton\u2019s method. SIAM J. Numer. Anal. 23, 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"1350_CR17","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1145\/962437.962439","volume":"29","author":"NIM Gould","year":"2003","unstructured":"Gould, N.I.M., Orban, D., Toint, PhL: CUTEr: a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 373\u2013394 (2003)","journal-title":"ACM Trans. Math. Softw."},{"key":"1350_CR18","doi-asserted-by":"publisher","first-page":"2158","DOI":"10.1016\/j.camwa.2007.08.038","volume":"55","author":"N Gu","year":"2008","unstructured":"Gu, N., Mo, J.: Incorporating nonmonotone strategies into the trust region method for unconstrained optimization. Comput. Math. Appl. 55, 2158\u20132172 (2008)","journal-title":"Comput. Math. Appl."},{"key":"1350_CR19","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1080\/00207160212121","volume":"79","author":"RR Khazal","year":"2002","unstructured":"Khazal, R.R.: Existence and stability of Choleski Q.I.F. for symmetric linear systems. Int. J. Comput. Math. 79, 1013\u20131023 (2002)","journal-title":"Int. J. Comput. Math."},{"key":"1350_CR20","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1023\/B:COAP.0000026881.96694.32","volume":"28","author":"DH Li","year":"2004","unstructured":"Li, D.H., Fukushima, M., Qi, L., Yamashita, N.: Regularized Newton methods for convex minimization problems with singular solutions. Comput. Optim. Appl. 28, 131\u2013147 (2004)","journal-title":"Comput. Optim. Appl."},{"key":"1350_CR21","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1145\/355934.355936","volume":"7","author":"JJ More","year":"1981","unstructured":"More, J.J., Grabow, B.S., Hillstrom, K.E.: testing unconstrained optimization software. ACM. Trans. Math. Softw. 7, 17\u201341 (1981)","journal-title":"ACM. Trans. Math. Softw."},{"key":"1350_CR22","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.: Numerical Optimization, 2nd edn. Springer, New York (2006)","edition":"2"},{"key":"1350_CR23","doi-asserted-by":"publisher","first-page":"1913","DOI":"10.1007\/s11590-011-0386-z","volume":"6","author":"Ch Shen","year":"2012","unstructured":"Shen, Ch., Xiongda, Ch., Liang, Y.: A regularized Newton method for degenerate unconstrained optimization problems. Optim. Lett. 6, 1913\u20131933 (2012)","journal-title":"Optim. Lett."},{"key":"1350_CR24","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s002459900128","volume":"40","author":"D Sun","year":"1999","unstructured":"Sun, D.: A regularization Newton method for solving nonlinear complementarity problems. Appl. Math. Optim. 40, 315\u2013339 (1999)","journal-title":"Appl. Math. Optim."},{"key":"1350_CR25","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s00245-009-9094-9","volume":"62","author":"K Ueda","year":"2010","unstructured":"Ueda, K., Yamashita, N.: Convergence properties of the regularized Newton method for the unconstrained nonconvex optimization. Appl. Math. Optim. 62, 27\u201346 (2010)","journal-title":"Appl. Math. Optim."},{"key":"1350_CR26","doi-asserted-by":"publisher","first-page":"7","DOI":"10.5539\/jmr.v7n2p7","volume":"7","author":"H Wang","year":"2015","unstructured":"Wang, H., Qin, M.: A regularized Newton method with correction for unconstrained nonconvex optimization. J. Math. Res. 7, 7\u201317 (2015)","journal-title":"J. Math. Res."},{"key":"1350_CR27","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1023\/A:1018957708498","volume":"87","author":"J Zhang","year":"1999","unstructured":"Zhang, J., Xu, C.: Trust region dogleg path algorithms for unconstrained minimization. Ann. Oper. Res. 87, 407\u2013418 (1999)","journal-title":"Ann. Oper. Res."},{"key":"1350_CR28","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"HC Zhang","year":"2004","unstructured":"Zhang, H.C., Hager, W.W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14, 1043\u20131056 (2004)","journal-title":"SIAM J. Optim."},{"key":"1350_CR29","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 eficient line search. SIAM J. Optim. 16, 170\u2013192 (2005)","journal-title":"SIAM J. Optim."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01350-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01350-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01350-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T00:20:38Z","timestamp":1618878038000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01350-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,20]]},"references-count":29,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["1350"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01350-7","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2020,4,20]]},"assertion":[{"value":"22 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}