{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T09:03:54Z","timestamp":1769850234045,"version":"3.49.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,5,1]],"date-time":"2006-05-01T00:00:00Z","timestamp":1146441600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2006,5]]},"DOI":"10.1007\/s11075-006-9023-9","type":"journal-article","created":{"date-parts":[[2006,6,20]],"date-time":"2006-06-20T10:24:03Z","timestamp":1150799043000},"page":"63-73","source":"Crossref","is-referenced-by-count":74,"title":["An acceleration of gradient descent algorithm with backtracking for unconstrained optimization"],"prefix":"10.1007","volume":"42","author":[{"given":"Neculai","family":"Andrei","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,6,21]]},"reference":[{"key":"9023_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2140\/pjm.1966.16.1","volume":"6","author":"L. Armijo","year":"1966","unstructured":"Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 6, 1\u20133 (1966)","journal-title":"Pac. J. Math."},{"key":"9023_CR2","doi-asserted-by":"crossref","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.L.: CUTE: Constrained and unconstrained testing environments. ACM Trans. Math. Softw. 21, 123\u2013160 (1995)","journal-title":"ACM Trans. Math. Softw."},{"key":"9023_CR3","first-page":"536","volume":"25","author":"A. Cauchy","year":"1848","unstructured":"Cauchy, A.: M\u00e9thodes g\u00e9n\u00e9rales pour la r\u00e9solution des syst\u00e9mes d\u00e9quations simultan\u00e9es. C. R. Acad. Sci., Paris 25, 536\u2013538 (1848)","journal-title":"C. R. Acad. Sci., Paris"},{"key":"9023_CR4","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"J.E. Dennis","year":"1983","unstructured":"Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewoods Cliffs, New Jersey (1983)"},{"key":"9023_CR5","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":"9023_CR6","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization. Wiley, New York (1987)"},{"key":"9023_CR7","first-page":"183","volume":"57","author":"G.E. Forsythe","year":"1951","unstructured":"Forsythe, G.E., Motzkin, T.S.: Asymptotic properties of the optimum gradient method. Bull. Am. Soc. 57, 183 (1951)","journal-title":"Bull. Am. Soc."},{"key":"9023_CR8","first-page":"147","volume":"3","author":"A.A. Goldstein","year":"1965","unstructured":"Goldstein, A.A.: On steepest descent. SIAM J. Control 3, 147\u2013151 (1965)","journal-title":"SIAM J. Control"},{"key":"9023_CR9","volume-title":"Recent Advances in Optimisation Techniques","author":"W.E. Humphrey","year":"1966","unstructured":"Humphrey, W.E.: A general minimising routine \u2013 minfun. In: Lavi, A., Vogl, T.P. (eds.) Recent Advances in Optimisation Techniques. Wiley, New York (1966)"},{"key":"9023_CR10","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BFb0004506","volume-title":"Optimization and Optimal Control","author":"C. Lemar\u00e9chal","year":"1981","unstructured":"Lemar\u00e9chal, C.: A view of line search. In: Auslander, A., Oettli, W., Stoer, J. (eds.) Optimization and Optimal Control, pp. 59\u201378. Springer, Berlin (1981)"},{"key":"9023_CR11","unstructured":"Mor\u00e9, J.J., Thuente, D.J.: On line search algorithms with guaranteed sufficient decrease. Mathematics and Computer Science Division Preprint MCS-P153-0590, Argonne National Laboratory, Argonne (1990)"},{"key":"9023_CR12","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/BF02193062","volume":"85","author":"F.A. Potra","year":"1995","unstructured":"Potra, F.A., Shi, Y.: Efficient line search algorithm for unconstrained optimization. J. Optim. Theory Appl. 85, 677\u2013704 (1995)","journal-title":"J. Optim. Theory Appl."},{"key":"9023_CR13","first-page":"53","volume":"9","author":"M.J.D. Powell","year":"1976","unstructured":"Powell, M.J.D.: Some global convergence properties of a variable-metric algorithm for minimization without exact line searches. SIAM-AMS Proc., Philadelphia 9, 53\u201372 (1976)","journal-title":"SIAM-AMS Proc., Philadelphia"},{"key":"9023_CR14","volume-title":"Recent Advances in Optimisation Techniques","author":"R. Schinzinger","year":"1966","unstructured":"Schinzinger, R.: Optimization in electromagnetic system design. In: Lavi, A., Vogl, T.P. (Eds.) Recent Advances in Optimisation Techniques. Wiley, New York (1966)"},{"key":"9023_CR15","first-page":"393","volume":"157","author":"S. Zhen-Jun","year":"2004","unstructured":"Zhen-Jun, S.: Convergence of line search methods for unconstrained optimization. Appl. Math. Comput. 157, 393\u2013405 (2004)","journal-title":"Appl. Math. Comput."},{"key":"9023_CR16","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1137\/1011036","volume":"11","author":"P. Wolfe","year":"1968","unstructured":"Wolfe, P.: Convergence conditions for ascent methods. SIAM Rev. 11, 226\u2013235 (1968)","journal-title":"SIAM Rev."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-006-9023-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-006-9023-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-006-9023-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:07Z","timestamp":1559351287000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-006-9023-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,5]]}},"alternative-id":["9023"],"URL":"https:\/\/doi.org\/10.1007\/s11075-006-9023-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,5]]}}}