{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T20:39:28Z","timestamp":1774557568034,"version":"3.50.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2009,9,4]],"date-time":"2009-09-04T00:00:00Z","timestamp":1252022400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2011,6]]},"DOI":"10.1007\/s10107-009-0305-6","type":"journal-article","created":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T09:17:47Z","timestamp":1251969467000},"page":"285-319","source":"Crossref","is-referenced-by-count":7,"title":["Combining and scaling descent and negative curvature directions"],"prefix":"10.1007","volume":"128","author":[{"given":"Catarina P.","family":"Avelino","sequence":"first","affiliation":[]},{"given":"Javier M.","family":"Moguerza","sequence":"additional","affiliation":[]},{"given":"Alberto","family":"Olivares","sequence":"additional","affiliation":[]},{"given":"Francisco J.","family":"Prieto","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,9,4]]},"reference":[{"key":"305_CR1","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1137\/0708060","volume":"8","author":"J.R. Bunch","year":"1971","unstructured":"Bunch J.R., Parlett B.N.: Direct methods for solving symmetric indefinite systems of linear equations. SIAM J. Numer. Anal. 8, 639\u2013655 (1971)","journal-title":"SIAM J. Numer. Anal."},{"key":"305_CR2","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/BF01580735","volume":"40","author":"R.H. Byrd","year":"1988","unstructured":"Byrd R.H., Schnabel R.B., Shultz G.A.: Approximate solution of the trust region problem by minimization over two-dimensional subspaces. Math. Program. 40, 247\u2013263 (1988)","journal-title":"Math. Program."},{"issue":"2","key":"305_CR3","doi-asserted-by":"crossref","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(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"305_CR4","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971316","volume-title":"Nonlinear Programming: Sequential Unconstrained Minimization Techniques","author":"A.V. Fiacco","year":"1990","unstructured":"Fiacco A.V., McCormick G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Society for Industrial and Applied Mathematics, Philadelphia (1990)"},{"key":"305_CR5","volume-title":"Practical Methods of Optimization, Volume 1, Unconstrained Optimization","author":"R. Fletcher","year":"1980","unstructured":"Fletcher R.: Practical Methods of Optimization, Volume 1, Unconstrained Optimization. Wiley, New York and Toronto (1980)"},{"key":"305_CR6","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1137\/0614040","volume":"14","author":"A. Forsgren","year":"1993","unstructured":"Forsgren A., Murray W.: Newton methods for large-scale linear equality-constrained minimization. SIAM J. Matrix Anal. Appl. 14, 560\u2013587 (1993)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"305_CR7","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/BF01585529","volume":"7","author":"P.E. Gill","year":"1974","unstructured":"Gill P.E., Murray W.: Newton type methods for unconstrained and linearly constrained optimization. Math. Program. 7, 311\u2013350 (1974)","journal-title":"Math. Program."},{"key":"305_CR8","volume-title":"Practical Optimization","author":"P.E. Gill","year":"1981","unstructured":"Gill P.E., Murray W., Wright M.H.: Practical Optimization. Academic Press, London and New York (1981)"},{"key":"305_CR9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF01588294","volume":"18","author":"D. Goldfarb","year":"1980","unstructured":"Goldfarb D.: Curvilinear path steplength algorithms for minimization which use directions of negative curvature. Math. Program. 18, 31\u201340 (1980)","journal-title":"Math. Program."},{"key":"305_CR10","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1080\/10556780008805794","volume":"14","author":"N.I.M. Gould","year":"2000","unstructured":"Gould N.I.M., Lucidi S., Roma M., Toint Ph.L.: Exploiting negative curvature directions in linesearch methods for unconstrained optimization. Optim. Methods Softw. 14, 75\u201398 (2000)","journal-title":"Optim. Methods Softw."},{"key":"305_CR11","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1145\/962437.962439","volume":"29","author":"N.I.M. Gould","year":"2003","unstructured":"Gould N.I.M., Orban D., Toint Ph.L.: CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 373\u2013394 (2003)","journal-title":"ACM Trans. Math. Softw."},{"key":"305_CR12","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":"305_CR13","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s10107-002-0360-8","volume":"95","author":"J.M. Moguerza","year":"2003","unstructured":"Moguerza J.M., Prieto F.J.: An augmented Lagrangian interior-point method using directions of negative curvature. Math. Program. 95, 573\u2013616 (2003)","journal-title":"Math. Program."},{"key":"305_CR14","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s10107-002-0367-1","volume":"96","author":"J.M. Moguerza","year":"2003","unstructured":"Moguerza J.M., Prieto F.J.: Combining search directions using gradient flows. Math. Program. 96, 529\u2013559 (2003)","journal-title":"Math. Program."},{"key":"305_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01582091","volume":"16","author":"J.J. Mor\u00e9","year":"1979","unstructured":"Mor\u00e9 J.J., Sorensen D.C.: On the use of directions of negative curvature in a modified Newton method. Math. Program. 16, 1\u201320 (1979)","journal-title":"Math. Program."},{"key":"305_CR16","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/BF00933150","volume":"26","author":"H. Mukai","year":"1978","unstructured":"Mukai H., Polak E.: A second-order method for the general nonlinear programming problem. J. Optim. Theory Appl. 26, 515\u2013532 (1978)","journal-title":"J. Optim. Theory Appl."},{"key":"305_CR17","unstructured":"Olivares, A., Moguerza, J.M., Prieto, F.J.: Nonconvex optimization using an adapted linesearch, Eur. J. Oper. Res. pages to be assigned, (2007)"},{"key":"305_CR18","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1023\/A:1022653904717","volume":"98","author":"S. Sanmat\u00edas","year":"1998","unstructured":"Sanmat\u00edas S., Vercher E.: A generalized conjugate gradient algorithm. J. Optim. Theory Appl. 98, 489\u2013502 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"305_CR19","volume-title":"Un m\u00e9todo de b\u00fasqueda Lineal con Direcciones Combinadas Para La Optimizaci\u00f3n Irrestringida","author":"S. Sanmat\u00edas","year":"2001","unstructured":"Sanmat\u00edas S., Roma M.: Un m\u00e9todo de b\u00fasqueda Lineal con Direcciones Combinadas Para La Optimizaci\u00f3n Irrestringida. Actas del XXVI Congreso Nacional de Estad\u00edstica e Investigaci\u00f3n Operativa, \u00dabeda, Spain (2001)"},{"key":"305_CR20","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.ejor.2003.04.003","volume":"164","author":"J. Sun","year":"2005","unstructured":"Sun J., Yang X., Chen X.: Quadratic cost flow and the conjugate gradient method. Eur. J. Oper. Res. 164, 104\u2013114 (2005)","journal-title":"Eur. J. Oper. Res."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0305-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-009-0305-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0305-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T09:50:07Z","timestamp":1559123407000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-009-0305-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,4]]},"references-count":20,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2011,6]]}},"alternative-id":["305"],"URL":"https:\/\/doi.org\/10.1007\/s10107-009-0305-6","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9,4]]}}}