{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:30:53Z","timestamp":1774276253469,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,2,21]],"date-time":"2013-02-21T00:00:00Z","timestamp":1361404800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2013,10]]},"DOI":"10.1007\/s10957-013-0285-9","type":"journal-article","created":{"date-parts":[[2013,2,20]],"date-time":"2013-02-20T20:54:34Z","timestamp":1361393674000},"page":"159-182","source":"Crossref","is-referenced-by-count":31,"title":["Another Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions for Large-scale Unconstrained Optimization"],"prefix":"10.1007","volume":"159","author":[{"given":"Neculai","family":"Andrei","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,2,21]]},"reference":[{"key":"285_CR1","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1137\/1031003","volume":"31","author":"G.H. Golub","year":"1989","unstructured":"Golub, G.H., O\u2019Leary, D.P.: Some history of the conjugate gradient and Lanczos algorithms: 1948\u20131976. SIAM Rev. 31, 50\u2013102 (1989)","journal-title":"SIAM Rev."},{"key":"285_CR2","first-page":"1","volume-title":"Linear and Nonlinear Conjugate Gradient\u2014Related Methods","author":"D.P. O\u2019Leary","year":"1996","unstructured":"O\u2019Leary, D.P.: Conjugate gradients and related KMP algorithms: the beginnings. In: Adams, L., Nazareth, J.L. (eds.) Linear and Nonlinear Conjugate Gradient\u2014Related Methods, pp. 1\u20138. SIAM, Philadelphia (1996)"},{"key":"285_CR3","first-page":"35","volume":"2","author":"W.W. Hager","year":"2006","unstructured":"Hager, W.W., Zhang, H.: A survey of nonlinear conjugate gradient methods. Pac. J. Optim. 2, 35\u201358 (2006)","journal-title":"Pac. J. Optim."},{"key":"285_CR4","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"E.D. Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"285_CR5","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":"285_CR6","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"M.R. Hestenes","year":"1952","unstructured":"Hestenes, M.R., Stiefel, E.L.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409\u2013436 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"285_CR7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1023\/A:1012930416777","volume":"103","author":"Y.H. Dai","year":"2001","unstructured":"Dai, Y.H., Yuan, Y.: An efficient hybrid conjugate gradient method for unconstrained optimization. Ann. Oper. Res. 103, 33\u201347 (2001)","journal-title":"Ann. Oper. Res."},{"key":"285_CR8","first-page":"35","volume":"16","author":"E. Polak","year":"1969","unstructured":"Polak, E., Ribi\u00e8re, G.: Note sur la convergence de directions conjugu\u00e9e. Rev. Fr. Inf. Rech. Oper. 16, 35\u201343 (1969)","journal-title":"Rev. Fr. Inf. Rech. Oper."},{"key":"285_CR9","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/0041-5553(69)90035-4","volume":"9","author":"B.T. 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":"285_CR10","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1137\/030601880","volume":"16","author":"W.W. 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, 170\u2013192 (2005)","journal-title":"SIAM J. Optim."},{"key":"285_CR11","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/BF01589116","volume":"45","author":"D.C. Liu","year":"1989","unstructured":"Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization methods. Math. Program. 45, 503\u2013528 (1989)","journal-title":"Math. Program."},{"key":"285_CR12","doi-asserted-by":"crossref","unstructured":"Averick, B.M., Carter, R.G., Mor\u00e9, J.J., Xue, G.L.: The MINPACK-2 test problem collection. Mathematics and Computer Science Division, Argonne National Laboratory, Preprint MCS-P153-0692 (1992)","DOI":"10.2172\/79972"},{"key":"285_CR13","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1137\/1011036","volume":"11","author":"P. Wolfe","year":"1969","unstructured":"Wolfe, P.: Convergence conditions for ascent methods. SIAM Rev. 11, 226\u2013235 (1969)","journal-title":"SIAM Rev."},{"key":"285_CR14","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1287\/opre.26.6.1073","volume":"26","author":"A. Perry","year":"1978","unstructured":"Perry, A.: A modified conjugate gradient algorithm. Oper. Res. 26, 1073\u20131078 (1978)","journal-title":"Oper. Res."},{"key":"285_CR15","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1287\/moor.3.3.244","volume":"3","author":"D.F. Shanno","year":"1978","unstructured":"Shanno, D.F.: Conjugate gradient methods with inexact searches. Math. Oper. Res. 3, 244\u2013256 (1978)","journal-title":"Math. Oper. Res."},{"key":"285_CR16","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s002450010019","volume":"43","author":"Y.H. Dai","year":"2001","unstructured":"Dai, Y.H., Liao, L.Z.: New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43, 87\u2013101 (2001)","journal-title":"Appl. Math. Optim."},{"key":"285_CR17","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s10589-007-9055-7","volume":"38","author":"N. Andrei","year":"2007","unstructured":"Andrei, N.: Scaled conjugate gradient algorithms for unconstrained optimization. Comput. Optim. Appl. 38, 401\u2013416 (2007)","journal-title":"Comput. Optim. Appl."},{"key":"285_CR18","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/10556780600822260","volume":"22","author":"N. Andrei","year":"2007","unstructured":"Andrei, N.: Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization. Optim. Methods Softw. 22, 561\u2013571 (2007)","journal-title":"Optim. Methods Softw."},{"key":"285_CR19","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s00245-001-0003-0","volume":"43","author":"E. Birgin","year":"2001","unstructured":"Birgin, E., Mart\u00ednez, J.M.: A spectral conjugate gradient method for unconstrained optimization. Appl. Math. Optim. 43, 117\u2013128 (2001)","journal-title":"Appl. Math. Optim."},{"key":"285_CR20","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1002\/zamm.19950750118","volume":"75","author":"Y. Yuan","year":"1995","unstructured":"Yuan, Y., Stoer, J.: A subspace study on conjugate gradient algorithms. Z. Angew. Math. Mech. 75, 69\u201377 (1995)","journal-title":"Z. Angew. Math. Mech."},{"key":"285_CR21","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1145\/355666.355673","volume":"2","author":"D.F. Shanno","year":"1976","unstructured":"Shanno, D.F., Phua, K.H.: Algorithm 500. Minimization of unconstrained multivariate functions. ACM Trans. Math. Softw. 2, 87\u201394 (1976)","journal-title":"ACM Trans. Math. Softw."},{"key":"285_CR22","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.amc.2009.03.020","volume":"213","author":"N. Andrei","year":"2009","unstructured":"Andrei, N.: Acceleration of conjugate gradient algorithms for unconstrained optimization. Appl. Math. Comput. 213, 361\u2013369 (2009)","journal-title":"Appl. Math. Comput."},{"key":"285_CR23","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1145\/192115.192132","volume":"20","author":"J.J. Mor\u00e9","year":"1994","unstructured":"Mor\u00e9, J.J., Thuente, D.J.: Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Softw. 20, 286\u2013307 (1994)","journal-title":"ACM Trans. Math. Softw."},{"key":"285_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12613-4","volume-title":"Numerical Methods for Nonlinear Variational Problems","author":"R. Glowinski","year":"1984","unstructured":"Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer, Berlin (1984)"},{"key":"285_CR25","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF01441967","volume":"3","author":"G. Cimatti","year":"1977","unstructured":"Cimatti, G.: On a problem of the theory of lubrication governed by a variational inequality. Appl. Math. Optim. 3, 227\u2013242 (1977)","journal-title":"Appl. Math. Optim."},{"key":"285_CR26","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0045-7825(86)90073-3","volume":"57","author":"J. Goodman","year":"1986","unstructured":"Goodman, J., Kohn, R., Reyna, L.: Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Eng. 57, 107\u2013127 (1986)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"285_CR27","volume-title":"The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts","author":"R. Aris","year":"1975","unstructured":"Aris, R.: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts. Oxford University Press, London (1975)"},{"key":"285_CR28","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4546-9","volume-title":"Mathematical Problems from Combustion Theory","author":"J. Bebernes","year":"1989","unstructured":"Bebernes, J., Eberly, D.: Mathematical Problems from Combustion Theory. Applied Mathematical Sciences, vol. 83. Springer, Berlin (1989)"},{"key":"285_CR29","volume-title":"Lectures on Minimal Surfaces","author":"J.C.C. Nitsche","year":"1989","unstructured":"Nitsche, J.C.C.: Lectures on Minimal Surfaces vol. 1. Cambridge University Press, Cambridge (1989)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0285-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-013-0285-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0285-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T23:28:46Z","timestamp":1562714926000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-013-0285-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,21]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["285"],"URL":"https:\/\/doi.org\/10.1007\/s10957-013-0285-9","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,21]]}}}