{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T12:41:28Z","timestamp":1772800888803,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2005,5,1]],"date-time":"2005-05-01T00:00:00Z","timestamp":1114905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Applic"],"published-print":{"date-parts":[[2005,5]]},"DOI":"10.1007\/s10589-005-1066-7","type":"journal-article","created":{"date-parts":[[2005,5,17]],"date-time":"2005-05-17T13:40:08Z","timestamp":1116337208000},"page":"31-55","source":"Crossref","is-referenced-by-count":95,"title":["Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems"],"prefix":"10.1007","volume":"31","author":[{"given":"E. G.","family":"Birgin","sequence":"first","affiliation":[]},{"given":"R. A.","family":"Castillo","sequence":"additional","affiliation":[]},{"given":"J. M.","family":"Mart\u00cdnez","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"1066_CR1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1093\/comjnl\/13.2.171","volume":"13","author":"R.R. Allran","year":"1970","unstructured":"R.R. Allran and S.E.J. Johnsen, \u201cAn algorithm for solving nonlinear programming problems subject to nonlinear inequality constraints,\u201d The Computer Journal, vol. 13, pp. 171\u2013177, 1970.","journal-title":"The Computer Journal"},{"key":"1066_CR2","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1287\/moor.24.3.645","volume":"24","author":"A. Auslender","year":"1999","unstructured":"A. Auslender, M. Teboulle, and S. Ben-Tiba, \u201cInterior proximal and multiplier methods based on second order homogeneous kernels,\u201d Mathematics of Operations Research, vol. 24, pp. 645\u2013668, 1999.","journal-title":"Mathematics of Operations Research"},{"key":"1066_CR3","unstructured":"A. Ben Tal, I. Yuzefovich, and M. Zibulevsky, \u201cPenalty\/barrier multiplier methods for minimax and constrained smooth convex programs,\u201d Research Report 9\/92, Optimization Laboratory, Faculty of Industrial Engineering Management, Technion, Haifa, Israel, 1992."},{"key":"1066_CR4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1137\/S1052623493259215","volume":"7","author":"A. Ben-Tal","year":"1997","unstructured":"A. Ben-Tal and M. Zibulevsky, \u201cPenalty\/barrier multiplier methods for convex programming problems,\u201d SIAM Journal on Optimization, vol. 7, pp. 347\u2013366, 1997.","journal-title":"SIAM Journal on Optimization"},{"key":"1066_CR5","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"D.P. Bertsekas","year":"1982","unstructured":"D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Academic Press: New York, 1982."},{"key":"1066_CR6","volume-title":"Nonlinear Programming","author":"D.P. Bertsekas","year":"1999","unstructured":"D.P. Bertsekas, Nonlinear Programming, 2nd edition, Athena Scientific: Belmont, MA, 1999.","edition":"2"},{"key":"1066_CR7","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1019928808826","volume":"23","author":"E.G. Birgin","year":"2002","unstructured":"E.G. Birgin and J.M. Mart\u00ednez, \u201cLarge-scale active-set box-constrained optimization method with spectral projected gradients,\u201d Computational Optimization and Applications, vol. 23, pp. 101\u2013125, 2002.","journal-title":"Computational Optimization and Applications"},{"key":"1066_CR8","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"E.G. Birgin","year":"2000","unstructured":"E.G. Birgin, J.M. Mart\u00ednez, and M. Raydan, \u201cNonmonotone spectral projected gradient methods on convex sets,\u201d SIAM Journal on Optimization, vol. 10, pp. 1196\u20131211, 2000.","journal-title":"SIAM Journal on Optimization"},{"key":"1066_CR9","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1145\/502800.502803","volume":"27","author":"E.G. Birgin","year":"2001","unstructured":"E.G. Birgin, J.M. Mart\u00ednez, and M. Raydan, \u201cAlgorithm 813: SPG\u2014Software for convex-constrained optimization,\u201d ACM Transactions on Mathematical Software, vol. 27, pp. 340\u2013349, 2001.","journal-title":"ACM Transactions on Mathematical Software"},{"key":"1066_CR10","volume-title":"Tese de Doutorado, COPPE","author":"R.A. Castillo","year":"1998","unstructured":"R.A. Castillo, \u201cM\u00e9todos de Lagrangiano Aumentado usando penalidades general-izadas para programa\u00e7\u00e3o n\u00e3o linear,\u201d Tese de Doutorado, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil, 1998."},{"key":"1066_CR11","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1137\/0728030","volume":"28","author":"A.R. Conn","year":"1991","unstructured":"A.R. Conn, N.I.M. Gould, and Ph.L. Toint, \u201cA globally convergent Augmented Lagrangian algorithm for optimization with general constraints and simple bounds,\u201d SIAM Journal on Numerical Analysis, vol. 28, pp. 545\u2013572, 1991.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"1066_CR12","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"E.D. Dolan","year":"2002","unstructured":"E.D. Dolan and J.J. Mor\u00e9, \u201cBenchmarking optimization software with performance profiles,\u201d Mathematical Programming, vol. 91, pp. 201\u2013213, 2002.","journal-title":"Mathematical Programming"},{"key":"1066_CR13","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1023\/A:1008700911674","volume":"14","author":"Z. Dost\u00e1l","year":"1999","unstructured":"Z. Dost\u00e1l, A. Friedlander, and S.A. Santos, \u201cAugmented Lagrangians with adaptive precision control for quadratic programming with equality constraints,\u201d Computational Optimization and Applications, vol. 14, pp. 37\u201353, 1999.","journal-title":"Computational Optimization and Applications"},{"key":"1066_CR14","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1137\/S1052623499362573","volume":"13","author":"Z. Dost\u00e1l","year":"2003","unstructured":"Z. Dost\u00e1l, A. Friedlander, and S.A. Santos, \u201cAugmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraints,\u201d SIAM Journal on Optimization, vol. 13, pp. 1120\u20131140, 2003.","journal-title":"SIAM Journal on Optimization"},{"key":"1066_CR15","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1016\/S0045-7825(00)00180-8","volume":"190","author":"Z. Dost\u00e1l","year":"2002","unstructured":"Z. Dost\u00e1l, F.A.M. Gomes, and S.A. Santos, \u201cSolution of contact problems by FETI domain decomposition with natural coarse space projection,\u201d Computational Method in Applied Mechanics and Engineering, vol. 190, pp. 1611\u20131627, 2002.","journal-title":"Computational Method in Applied Mechanics and Engineering"},{"key":"1066_CR16","volume-title":"Practical Methods for Optimization","author":"R. Fletcher","year":"1987","unstructured":"R. Fletcher, Practical Methods for Optimization, John Wiley and Sons: Chichester, 1987."},{"key":"1066_CR17","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10107-002-0332-z","volume":"96","author":"C.C. Gonzaga","year":"2003","unstructured":"C.C. Gonzaga and R.A. Castillo, \u201cA nonlinear programming algorithm based on non-coercive penalty functions,\u201d Mathematical Programming, vol. 96, pp. 87\u2013101, 2003.","journal-title":"Mathematical Programming"},{"key":"1066_CR18","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF00939044","volume":"55","author":"W.W. Hager","year":"1987","unstructured":"W.W. Hager, \u201cDual techniques for constrained optimization,\u201d Journal of Optimization Theory and Applications, vol. 55, pp. 33\u201372, 1987.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1066_CR19","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF00940552","volume":"79","author":"W.W. Hager","year":"1993","unstructured":"W.W. Hager, \u201cAnalysis and implementation of a dual algorithm for constrained optimization,\u201d Journal of Optimization Theory and Applications, vol. 79, pp. 427\u2013462, 1993.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1066_CR20","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"M.R. Hestenes","year":"1969","unstructured":"M.R. Hestenes, \u201cMultiplier and gradient methods,\u201d Journal of Optimization Theory and Applications, vol 4, pp. 303\u2013320, 1969.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1066_CR21","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1051\/ro:2000102","volume":"34","author":"C. Humes","year":"2000","unstructured":"C. Humes and P.S. Silva, \u201cStrict convex regularizations, proximal points and Augmented Lagrangians,\u201d RAIRO Operations Research, vol. 34, pp. 283\u2013303, 2000.","journal-title":"RAIRO Operations Research"},{"key":"1066_CR22","first-page":"11","volume":"8","author":"A.N. Iusem","year":"1999","unstructured":"A.N. Iusem, \u201cAugmented Lagrangian methods and proximal point methods for convex optimization,\u201d Investigacion Operativa, vol. 8, pp. 11\u201350, 1999.","journal-title":"Investigacion Operativa"},{"key":"1066_CR23","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1137\/S0363012995281742","volume":"35","author":"K.C. Kiwiel","year":"1997","unstructured":"K.C. Kiwiel, \u201cProximal minimization methods with generalized Bregman functions,\u201d SIAM Journal on Control and Optimization, vol. 35, pp. 1142\u20131168, 1997.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"1066_CR24","doi-asserted-by":"crossref","unstructured":"B.W. Kort and D.P. Bertsekas, \u201cMultiplier methods for convex programming,\u201d in Proceeding of the IEEE Decision and Control Conference, San Diego, CA, 1973, pp. 260\u2013264.","DOI":"10.1109\/CDC.1973.269203"},{"key":"1066_CR25","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0314020","volume":"14","author":"B.W. Kort","year":"1976","unstructured":"B.W. Kort and D.P. Bertsekas, \u201cCombined primal-dual and penalty methods for convex programming,\u201d SIAM Journal on Control and Optimization, vol. 14, pp. 268\u2013294, 1976.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"1066_CR26","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0022-247X(67)90163-1","volume":"17","author":"O.L. Mangasarian","year":"1967","unstructured":"O.L. Mangasarian and S. Fromovitz, \u201cThe Fritz-John necessary optimality conditons in presence of equality and inequality constraints,\u201d Journal of Mathematical Analysis and Applications, vol. 17, pp. 37\u201347, 1967.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"1066_CR27","volume-title":"Tese de Doutorado","author":"L.C. Matioli","year":"2001","unstructured":"L.C. Matioli, \u201cUma nova metodologia para constru\u00e7\u00e3o de fun\u00e7\u00f5es de penaliza\u00e7\u00e3o para algoritoms de Lagrangiano Aumentado,\u201d Tese de Doutorado, Universidade Federal de Santa Catarina, Florian\u00f3polis, Brasil, 2001."},{"key":"1066_CR28","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1137\/0312052","volume":"12","author":"F.H. Murphy","year":"1974","unstructured":"F.H. Murphy, \u201cA class of exponential penalty functions,\u201d SIAM Journal on Control, vol. 12, pp. 679\u2013687, 1974.","journal-title":"SIAM Journal on Control"},{"key":"1066_CR29","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF00933876","volume":"17","author":"H. Nakayama","year":"1975","unstructured":"H. Nakayama, H. Samaya, and Y. Sawaragi, \u201cA generalized Lagrangian function and multiplier method,\u201d Journal of Optimization Theory and Applications, vol. 17, pp. 211\u2013227, 1975.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1066_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J. Nocedal","year":"1999","unstructured":"J. Nocedal and S.J. Wright, Numerical Optimization, Springer Verlag: New York, 1999."},{"key":"1066_CR31","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1023\/A:1010938423538","volume":"101","author":"R.A. Polyak","year":"2001","unstructured":"R.A. Polyak, \u201cLog-sigmoid multiplier method in constrained optimization,\u201d Annals of Operation Research, vol. 101, pp. 427\u2013460, 2001.","journal-title":"Annals of Operation Research"},{"key":"1066_CR32","first-page":"265","volume":"76","author":"R. Polyak","year":"1997","unstructured":"R. Polyak and M. Teboulle, \u201cNonliner rescaling and proximal-like methods in convex optimization,\u201d Mathematical Programming, vol. 76, pp. 265\u2013284, 1997.","journal-title":"Mathematical Programming"},{"key":"1066_CR33","first-page":"283","volume-title":"Optimization","author":"M.J.D. Powell","year":"1969","unstructured":"M.J.D. Powell, \u201cA method for nonlinear constraints in minimization problems,\u201d in Optimization, R. Fletcher (Ed.), Academic Press, New York, NY, 1969, pp. 283\u2013298."},{"key":"1066_CR34","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF00934777","volume":"12","author":"R.T. Rockafellar","year":"1973","unstructured":"R.T. Rockafellar, \u201cThe multiplier method of Hestenes and Powell applied to convex programming,\u201d Journal of Optimization Theory and Applications, vol. 12, pp. 555\u2013562, 1973.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1066_CR35","first-page":"670","volume":"17","author":"P. Tseng","year":"1993","unstructured":"P. Tseng and D. Bertseaks, \u201cOn the convergence of the exponential multiplier method for convex programming,\u201d Mathematical Programming, vol. 17, pp. 670\u2013690, 1993.","journal-title":"Mathematical Programming"},{"key":"1066_CR36","volume-title":"Tese de Doutorado, COPPE","author":"A.E. Xavier","year":"1992","unstructured":"A.E. Xavier, \u201cPenaliza\u00e7\u00e3o hiperbolica,\u201d Tese de Doutorado, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil, 1992."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-005-1066-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-005-1066-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-005-1066-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:27Z","timestamp":1559302587000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-005-1066-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,5]]}},"alternative-id":["1066"],"URL":"https:\/\/doi.org\/10.1007\/s10589-005-1066-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5]]}}}