{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T20:21:01Z","timestamp":1776284461025,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,3,25]],"date-time":"2009-03-25T00:00:00Z","timestamp":1237939200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s10589-009-9240-y","type":"journal-article","created":{"date-parts":[[2009,3,24]],"date-time":"2009-03-24T19:29:04Z","timestamp":1237922944000},"page":"209-236","source":"Crossref","is-referenced-by-count":34,"title":["Second-order negative-curvature methods for\u00a0box-constrained and general constrained optimization"],"prefix":"10.1007","volume":"45","author":[{"given":"R.","family":"Andreani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. G.","family":"Birgin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. M.","family":"Mart\u00ednez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. L.","family":"Schuverdt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,3,25]]},"reference":[{"key":"9240_CR1","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s10957-004-1861-9","volume":"125","author":"R. Andreani","year":"2005","unstructured":"Andreani, R., Mart\u00ednez, J.M., Schuverdt, M.L.: On the relation between the Constant Positive Linear Dependence condition and quasinormality constraint qualification. J.\u00a0Optim. Theory Appl. 125, 473\u2013485 (2005)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9240_CR2","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1137\/060654797","volume":"18","author":"R. Andreani","year":"2007","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: On Augmented Lagrangian Methods with general lower-level constraints. SIAM J. Optim. 18, 1286\u20131309 (2007)","journal-title":"SIAM J. Optim."},{"key":"9240_CR3","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1080\/02331930701618617","volume":"56","author":"R. Andreani","year":"2007","unstructured":"Andreani, R., Mart\u00ednez, J.M., Schuverdt, M.L.: On second-order optimality conditions for nonlinear programming. Optimization 56, 529\u2013542 (2007)","journal-title":"Optimization"},{"key":"9240_CR4","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/02331930500100270","volume":"54","author":"M. Andretta","year":"2005","unstructured":"Andretta, M., Birgin, E.G., Mart\u00ednez, J.M.: Practical active-set Euclidean trust-region method with spectral projected gradients for bound-constrained minimization. Optimization 54, 305\u2013325 (2005)","journal-title":"Optimization"},{"key":"9240_CR5","doi-asserted-by":"crossref","unstructured":"Anitescu, M.: Degenerate nonlinear programming with a quadratic growth condition. SIAM J. Optim. 1116\u20131135 (2000)","DOI":"10.1137\/S1052623499359178"},{"key":"9240_CR6","first-page":"49","volume":"15","author":"E.G. Birgin","year":"2001","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: A box constrained optimization algorithm with negative curvature directions and spectral projected gradients. Computing (Suppl.) 15, 49\u201360 (2001)","journal-title":"Computing (Suppl.)"},{"key":"9240_CR7","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1019928808826","volume":"23","author":"E.G. Birgin","year":"2002","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl. 23, 101\u2013125 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9240_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10589-007-9050-z","volume":"39","author":"E.G. Birgin","year":"2008","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Structured minimal-memory inexact quasi-Newton method and secant preconditioners for Augmented Lagrangian optimization. Comput. Optim. Appl. 39, 1\u201316 (2008)","journal-title":"Comput. Optim. Appl."},{"key":"9240_CR9","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"E.G. Birgin","year":"2000","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196\u20131211 (2000)","journal-title":"SIAM J. Optim."},{"key":"9240_CR10","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1145\/502800.502803","volume":"27","author":"E.G. Birgin","year":"2001","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Algorithm\u00a0813: SPG\u2014Software for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340\u2013349 (2001)","journal-title":"ACM Trans. Math. Softw."},{"key":"9240_CR11","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/imanum\/23.4.539","volume":"23","author":"E.G. Birgin","year":"2003","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Inexact Spectral Projected Gradient methods on convex sets. IMA J. Numer. Anal. 23, 539\u2013559 (2003)","journal-title":"IMA J. Numer. Anal."},{"key":"9240_CR12","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1137\/0724076","volume":"24","author":"R.H. Byrd","year":"1987","unstructured":"Byrd, R.H., Schnabel, R.B., Shultz, G.A.: A trust region algorithm for nonlinearly constrained optimization. SIAM J. Numer. Anal. 24, 1152\u20131170 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"9240_CR13","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1023\/A:1013764800871","volume":"21","author":"T.F. Coleman","year":"2002","unstructured":"Coleman, T.F., Liu, J., Yuan, W.: A new trust-region algorithm for equality constrained optimization. Comput. Optim. Appl. 21, 177\u2013199 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9240_CR14","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s101070050112","volume":"87","author":"A.R. Conn","year":"2000","unstructured":"Conn, A.R., Gould, N.I.M., Orban, D., Toint, Ph.L.: A primal-dual trust region algorithm for non-convex nonlinear programming. Math. Program. 87, 215\u2013249 (2000)","journal-title":"Math. Program."},{"key":"9240_CR15","series-title":"MPS\/SIAM Series on Optimization","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust Region Methods","author":"A.R. Conn","year":"2000","unstructured":"Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust Region Methods. MPS\/SIAM Series on Optimization. SIAM, Philadelphia (2000)"},{"key":"9240_CR16","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1137\/S1052623494278347","volume":"7","author":"J.E. Dennis","year":"1997","unstructured":"Dennis, J.E., Vicente, L.N.: On the convergence theory of trust-region-based algorithms for equality-constrained optimization. SIAM J. Optim. 7, 527\u2013550 (1997)","journal-title":"SIAM J. Optim."},{"key":"9240_CR17","doi-asserted-by":"crossref","first-page":"1750","DOI":"10.1137\/S036012995279031","volume":"36","author":"J.E. Dennis","year":"1998","unstructured":"Dennis, J.E., Heinkenschloss, M., Vicente, L.N.: Trust-region interior-point SQP algorithms for a class of nonlinear programming problems. SIAM J. Control Optim. 36, 1750\u20131794 (1998)","journal-title":"SIAM J. Control Optim."},{"key":"9240_CR18","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1287\/moor.1050.0150","volume":"30","author":"G. Di Pillo","year":"2005","unstructured":"Di Pillo, G., Lucidi, S., Palagi, L.: Convergence to second-order stationary points of a primal-dual algorithm model for nonlinear programming. Math. Oper. Res. 30, 897\u2013915 (2005)","journal-title":"Math. Oper. Res."},{"key":"9240_CR19","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1287\/moor.23.3.746","volume":"23","author":"F. Facchinei","year":"1998","unstructured":"Facchinei, F., Lucidi, S.: Convergence to second order stationary points in inequality constrained optimization. Math. Oper. Res. 23, 746\u2013766 (1998)","journal-title":"Math. Oper. Res."},{"key":"9240_CR20","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization. Wiley, New York (1987)"},{"key":"9240_CR21","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1137\/S1052623494279122","volume":"7","author":"A. Forsgren","year":"1997","unstructured":"Forsgren, A., Murray, W.: Newton methods for large-scale linear inequality constrained problems. SIAM J. Optim. 7, 132\u2013176 (1997)","journal-title":"SIAM J. Optim."},{"key":"9240_CR22","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":"9240_CR23","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":"9240_CR24","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1137\/050635225","volume":"17","author":"W.W. Hager","year":"2006","unstructured":"Hager, W.W., Zhang, H.C.: A new active set algorithm for box constrained optimization. SIAM J. Optim. 17, 526\u2013557 (2006)","journal-title":"SIAM J. Optim."},{"key":"9240_CR25","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"M.R. Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4, 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"9240_CR26","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1070\/RM1978v033n06ABEH003885","volume":"33","author":"E.S. Levitin","year":"1978","unstructured":"Levitin, E.S., Milyutin, A.A., Osmolovskii, N.P.: Higher order conditions for a local minimum in problems with constraints. Russian Math. Surv. 33, 97\u2013168 (1978)","journal-title":"Russian Math. Surv."},{"key":"9240_CR27","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0022-247X(67)90163-1","volume":"17","author":"O.L. Mangasarian","year":"1967","unstructured":"Mangasarian, O.L., Fromovitz, S.: The Fritz-John necessary optimality conditions in presence of equality and inequality constraints. J.\u00a0Math. Anal. Appl. 17, 37\u201347 (1967)","journal-title":"J.\u00a0Math. Anal. Appl."},{"key":"9240_CR28","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/BF01584328","volume":"13","author":"G.P. Mccormick","year":"1977","unstructured":"Mccormick, G.P.: A modification of Armijo\u2019s step-size rule for negative curvature. Math. Program. 13, 111\u2013115 (1977)","journal-title":"Math. Program."},{"key":"9240_CR29","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":"9240_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J. Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)"},{"key":"9240_CR31","first-page":"283","volume-title":"Optimization","author":"M.J.D. Powell","year":"1969","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283\u2013298. Academic Press, New York (1969)"},{"key":"9240_CR32","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1137\/S1052623497326629","volume":"10","author":"L. Qi","year":"2000","unstructured":"Qi, L., Wei, Z.: On the constant positive linear dependence condition and its application to SQP methods. SIAM J. Optim. 10, 963\u2013981 (2000)","journal-title":"SIAM J. Optim."},{"key":"9240_CR33","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"R.T. Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control Optim. 12, 268\u2013285 (1974)","journal-title":"SIAM J. Control Optim."},{"key":"9240_CR34","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/1035044","volume":"35","author":"R.T. Rockafellar","year":"1993","unstructured":"Rockafellar, R.T.: Lagrange multipliers and optimality. SIAM Rev. 35, 183\u2013238 (1993)","journal-title":"SIAM Rev."},{"key":"9240_CR35","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1137\/0722003","volume":"22","author":"G.A. Shultz","year":"1985","unstructured":"Shultz, G.A., Schnabel, R.B., Byrd, R.H.: A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties. SIAM J. Numer. Anal. 22, 47\u201367 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"9240_CR36","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1137\/0719026","volume":"19","author":"D.C. Sorensen","year":"1982","unstructured":"Sorensen, D.C.: Newton\u2019s method with a model trust region modification. SIAM J. Numer. Anal. 19, 409\u2013426 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"9240_CR37","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A. W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25\u201357 (2006)","journal-title":"Math. Program."},{"key":"9240_CR38","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1137\/S105262349627523X","volume":"9","author":"J. Zhang","year":"1999","unstructured":"Zhang, J., Xu, C.: A class of indefinite dogleg path methods for unconstrained minimization. SIAM J. Optim. 9, 646\u2013667 (1999)","journal-title":"SIAM J. Optim."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9240-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-009-9240-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9240-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:36Z","timestamp":1559302596000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-009-9240-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,25]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["9240"],"URL":"https:\/\/doi.org\/10.1007\/s10589-009-9240-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3,25]]}}}