{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T22:34:15Z","timestamp":1769639655866,"version":"3.49.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,10,3]],"date-time":"2018-10-03T00:00:00Z","timestamp":1538524800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s10589-018-0038-7","type":"journal-article","created":{"date-parts":[[2018,10,3]],"date-time":"2018-10-03T14:56:40Z","timestamp":1538578600000},"page":"215-239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A globally convergent Levenberg\u2013Marquardt method for equality-constrained optimization"],"prefix":"10.1007","volume":"72","author":[{"given":"A. F.","family":"Izmailov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. V.","family":"Solodov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. I.","family":"Uskov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,10,3]]},"reference":[{"key":"38_CR1","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"DP Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1982)"},{"key":"38_CR2","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/BF00933831","volume":"36","author":"DP Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Enlarging the region of convergence of Newton\u2019s method for constrained optimization. J. Optim. Theory Appl. 36, 221\u2013252 (1982)","journal-title":"J. Optim. Theory Appl."},{"key":"38_CR3","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1137\/0317044","volume":"17","author":"G Pillo Di","year":"1979","unstructured":"Di Pillo, G., Grippo, L.: A new class of augmented Lagrangians in nonlinear programming. SIAM J. Control Optim. 17, 618\u2013628 (1979)","journal-title":"SIAM J. Control Optim."},{"key":"38_CR4","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":"38_CR5","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s00186-012-0419-0","volume":"77","author":"F Facchinei","year":"2013","unstructured":"Facchinei, F., Fischer, A., Herrich, M.: A family of Newton methods for nonsmooth constrained systems with nonisolated solutions. Math. Methods Oper. Res. 77, 433\u2013443 (2013)","journal-title":"Math. Methods Oper. Res."},{"key":"38_CR6","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s00607-004-0083-1","volume":"74","author":"J-Y Fan","year":"2005","unstructured":"Fan, J.-Y., Yuan, Y.-X.: On the quadratic convergence of the Levenberg\u2013Marquardt method. Computing 74, 23\u201339 (2005)","journal-title":"Computing"},{"key":"38_CR7","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s10589-012-9502-y","volume":"54","author":"D Fern\u00e1ndez","year":"2013","unstructured":"Fern\u00e1ndez, D., Pilotta, E.A., Torres, G.A.: An inexact restoration strategy for the globalization of the sSQP method. Comput. Optim. Appl. 54, 595\u2013617 (2013)","journal-title":"Comput. Optim. Appl."},{"key":"38_CR8","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10107-008-0255-4","volume":"125","author":"D Fern\u00e1ndez","year":"2010","unstructured":"Fern\u00e1ndez, D., Solodov, M.: Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems. Math. Program. 125, 47\u201373 (2010)","journal-title":"Math. Program."},{"key":"38_CR9","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s10589-015-9782-0","volume":"63","author":"A Fischer","year":"2016","unstructured":"Fischer, A., Herrich, M., Izmailov, A.F., Solodov, M.V.: Convergence conditions for Newton-type methods applied to complementarity systems with nonisolated solutions. Comput. Optim. Appl. 63, 425\u2013459 (2016)","journal-title":"Comput. Optim. Appl."},{"key":"38_CR10","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1093\/imanum\/drw004","volume":"37","author":"PE Gill","year":"2017","unstructured":"Gill, P.E., Kungurtsev, V., Robinson, D.P.: A stabilized SQP method: global convergence. IMA J. Numer. Anal. 37, 407\u2013443 (2017)","journal-title":"IMA J. Numer. Anal."},{"key":"38_CR11","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1008640419184","volume":"12","author":"WW Hager","year":"1999","unstructured":"Hager, W.W.: Stabilized sequential quadratic programming. Comput. Optimizat. Appl. 12, 253\u2013273 (1999)","journal-title":"Comput. Optimizat. Appl."},{"key":"38_CR12","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s10107-007-0158-9","volume":"117","author":"AF Izmailov","year":"2009","unstructured":"Izmailov, A.F., Solodov, M.V.: On attraction of Newton-type iterates to multipliers violating second-order sufficiency conditions. Math. Program. 117, 271\u2013304 (2009)","journal-title":"Math. Program."},{"key":"38_CR13","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s10107-010-0413-3","volume":"133","author":"AF Izmailov","year":"2012","unstructured":"Izmailov, A.F., Solodov, M.V.: Stabilized SQP revisited. Math. Program. 133, 93\u2013120 (2012)","journal-title":"Math. Program."},{"key":"38_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11750-015-0372-1","volume":"23","author":"AF Izmailov","year":"2015","unstructured":"Izmailov, A.F., Solodov, M.V.: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it. TOP 23, 1\u201326 (2015)","journal-title":"TOP"},{"key":"38_CR15","volume-title":"Newton-Type Methods for Optimization and Variational Problems. Springer Series in Operations Research and Financial Engineering","author":"AF Izmailov","year":"2014","unstructured":"Izmailov, A.F., Solodov, M.V.: Newton-Type Methods for Optimization and Variational Problems. Springer Series in Operations Research and Financial Engineering. Springer, Basel (2014)"},{"key":"38_CR16","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s10589-015-9744-6","volume":"62","author":"AF Izmailov","year":"2015","unstructured":"Izmailov, A.F., Solodov, M.V., Uskov, E.I.: Combining stabilized SQP with the augmented Lagrangian algorithm. Comput. Optim. Appl. 62, 405\u2013429 (2015)","journal-title":"Comput. Optim. Appl."},{"key":"38_CR17","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/s10957-016-0889-y","volume":"169","author":"AF Izmailov","year":"2016","unstructured":"Izmailov, A.F., Solodov, M.V., Uskov, E.I.: Globalizing stabilized sequential quadratic programming method by smooth primal\u2013dual exact penalty function. J. Optim. Theory Appl. 169, 148\u2013178 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"38_CR18","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10589-016-9890-5","volume":"67","author":"AF Izmailov","year":"2017","unstructured":"Izmailov, A.F., Uskov, E.I.: Subspace-stabilized sequential quadratic programming. Comput. Optim. Appl. 67, 129\u2013154 (2017)","journal-title":"Comput. Optim. Appl."},{"key":"38_CR19","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization, Second edn. Springer, New York (2006)","edition":"Second"},{"key":"38_CR20","unstructured":"SQPlab. \n                    https:\/\/who.rocq.inria.fr\/Jean-Charles.Gilbert\/modulopt\/optimization-routines\/sqplab\/sqplab.html\n                    \n                  . Accessed Dec 2006"},{"key":"38_CR21","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1018665102534","volume":"11","author":"SJ Wright","year":"1998","unstructured":"Wright, S.J.: Superlinear convergence of a stabilized SQP method to a degenerate solution. Comput. Optim. Appl. 11, 253\u2013275 (1998)","journal-title":"Comput. Optim. Appl."},{"key":"38_CR22","first-page":"470","volume":"13","author":"SJ Wright","year":"2002","unstructured":"Wright, S.J.: Modifying SQP for degenerate problems SIAM. J. Optim. 13, 470\u2013497 (2002)","journal-title":"J. Optim."},{"key":"38_CR23","first-page":"237","volume":"15","author":"N Yamashita","year":"2001","unstructured":"Yamashita, N., Fukushima, M.: On the rate of convergence of the Levenberg\u2013Marquardt method. Comput. Suppl. 15, 237\u2013249 (2001)","journal-title":"Comput. Suppl."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-018-0038-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-018-0038-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-018-0038-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T23:22:10Z","timestamp":1570058530000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-018-0038-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,3]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["38"],"URL":"https:\/\/doi.org\/10.1007\/s10589-018-0038-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,3]]},"assertion":[{"value":"8 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 October 2018","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}