{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T08:51:36Z","timestamp":1762505496550},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,7,28]],"date-time":"2009-07-28T00:00:00Z","timestamp":1248739200000},"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":[[2011,5]]},"DOI":"10.1007\/s10589-009-9279-9","type":"journal-article","created":{"date-parts":[[2009,7,27]],"date-time":"2009-07-27T15:24:22Z","timestamp":1248708262000},"page":"61-99","source":"Crossref","is-referenced-by-count":11,"title":["A class of nonlinear Lagrangians for nonconvex second order cone programming"],"prefix":"10.1007","volume":"49","author":[{"given":"Liwei","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiantao","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,7,28]]},"reference":[{"key":"9279_CR1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1287\/moor.22.1.43","volume":"22","author":"A. Auslender","year":"1997","unstructured":"Auslender, A., Cominetti, R., Haddou, M.: Asymptotic analysis of penalty and barrier methods in convex and linear programming. Math. Oper. Res. 22, 43\u201362 (1997)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"9279_CR2","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1137\/S1052623493259215","volume":"7","author":"A. Ben-Tel","year":"1997","unstructured":"Ben-Tel, A., Zibulevsky, M.: Penalty\/barrier multiplier methods for convex programming problems. SIAM J. Optim. 7(2), 347\u2013366 (1997)","journal-title":"SIAM J. Optim."},{"key":"9279_CR3","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"D.P. Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1982)"},{"key":"9279_CR4","volume-title":"Nonlinear Programming","author":"D.P. Bertsekas","year":"1999","unstructured":"Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1999)","edition":"2"},{"key":"9279_CR5","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10107-005-0613-4","volume":"104","author":"J.F. Bonnans","year":"2005","unstructured":"Bonnans, J.F., Ram\u00edrez, C.H.: Perturbation analysis of second order cone programming problems. Math. Program., Ser. B 104, 205\u2013227 (2005)","journal-title":"Math. Program., Ser. B"},{"key":"9279_CR6","doi-asserted-by":"crossref","unstructured":"Breitfeld, M., Shanno, D.: A globally convergent penalty-barrier algorithm for nonlinear programming and its computational performance. Technical Report, Rutcor Research Report, Rutgers University, New Jersey (1994)","DOI":"10.1007\/978-3-642-79459-9_5"},{"key":"9279_CR7","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF01593788","volume":"12","author":"C. Charalambous","year":"1977","unstructured":"Charalambous, C.: Nonlinear least pth optimization and nonlinear programming. Math. Program. 12, 195\u2013225 (1977)","journal-title":"Math. Program."},{"key":"9279_CR8","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/s10107-003-0459-6","volume":"99","author":"J.P. Dussault","year":"2004","unstructured":"Dussault, J.P.: Augmented non-quadratic penalty algorithms. Math. Program. 99, 467\u2013486 (2004)","journal-title":"Math. Program."},{"key":"9279_CR9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534778.001.0001","volume-title":"Analysis on Symmetric Cones","author":"J. Faraut","year":"1994","unstructured":"Faraut, J., Kor\u00e1nyi, A.: Analysis on Symmetric Cones. Clarendon, Oxford (1994)"},{"key":"9279_CR10","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1137\/S1052623400380365","volume":"12","author":"M. Fukushima","year":"2001","unstructured":"Fukushima, M., Luo, Z.-Q., Tseng, P.: Smoothing functions for second-order-cone complementarity problems. SIAM J. Optim. 12, 436\u2013460 (2001)","journal-title":"SIAM J. Optim."},{"key":"9279_CR11","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s10107-005-0603-6","volume":"106","author":"I. Griva","year":"2006","unstructured":"Griva, I., Polyak, R.A.: Primal-dual nonlinear rescaling method with dynamic scaling parameter update. Math. Program. 106, 237\u2013259 (2006)","journal-title":"Math. Program."},{"key":"9279_CR12","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1137\/S1052623403421516","volume":"15","author":"S. Hayashi","year":"2005","unstructured":"Hayashi, S., Yamashita, N., Fukushima, M.: A combined smoothing and regularization method for monotone second-order cone complementarity problems. SIAM J. Optim. 15, 593\u2013615 (2005)","journal-title":"SIAM J. Optim."},{"key":"9279_CR13","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 method. J. Optim. Theory Appl. 4, 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"9279_CR14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s11590-006-0009-2","volume":"1","author":"H. Kato","year":"2007","unstructured":"Kato, H., Fukushima, M.: An SQP-type algorithm for nonlinear second-order cone programs. Optim. Lett. 1, 129\u2013144 (2007)","journal-title":"Optim. Lett."},{"key":"9279_CR15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF02192229","volume":"85","author":"D. Li","year":"1995","unstructured":"Li, D.: Zero duality gap for a class of nonconvex optimization problems. J. Optim. Theory Appl. 85, 309\u2013323 (1995)","journal-title":"J. Optim. Theory Appl."},{"key":"9279_CR16","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1016\/j.na.2006.07.022","volume":"67","author":"Y.J. Liu","year":"2007","unstructured":"Liu, Y.J., Zhang, L.W.: Convergence analysis of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Nonlinear Anal. 67, 1359\u20131373 (2007)","journal-title":"Nonlinear Anal."},{"key":"9279_CR17","author":"Y.J. Liu","year":"2008","unstructured":"Liu, Y.J., Zhang, L.W.: On the approximate augmented Lagrangian for nonlinear second order cone programming. Nonlinear Anal. Theory Methods Appl. (2008). doi: 10.1016\/j.na.2006.12.016","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"9279_CR18","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1137\/0313045","volume":"13","author":"O.L. Mangasarian","year":"1975","unstructured":"Mangasarian, O.L.: Unconstrained Lagrangians in nonlinear programming. SIAM J. Control 13, 772\u2013791 (1975)","journal-title":"SIAM J. Control"},{"key":"9279_CR19","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01586050","volume":"54","author":"R.A. Polyak","year":"1992","unstructured":"Polyak, R.A.: Modified barrier function: theory and methods. Math. Program. 54, 177\u2013222 (1992)","journal-title":"Math. Program."},{"key":"9279_CR20","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1023\/A:1010938423538","volume":"101","author":"R.A. Polyak","year":"2001","unstructured":"Polyak, R.A.: Log-Sigmoid multipliers method in constrained optimization. Ann. Oper. Res. 101, 427\u2013460 (2001)","journal-title":"Ann. Oper. Res."},{"key":"9279_CR21","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s101070100293","volume":"92","author":"R.A. Polyak","year":"2002","unstructured":"Polyak, R.A.: Nonlinear rescaling vs. smoothing technique in convex optimization. Math. Program. 92, 197\u2013235 (2002)","journal-title":"Math. Program."},{"key":"9279_CR22","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1023\/B:JOTA.0000041733.24606.99","volume":"122","author":"R.A. Polyak","year":"2004","unstructured":"Polyak, R.A., Griva, I.: Primal-Dual nonlinear rescaling method for convex optimization. J. Optim. Theory Appl. 122, 111\u2013156 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"9279_CR23","first-page":"265","volume":"76","author":"R.A. Polyak","year":"1997","unstructured":"Polyak, R.A., Teboulle, M.: Nonlinear rescaling and proximal-like methods in convex optimization. Math. Program. 76, 265\u2013284 (1997)","journal-title":"Math. Program."},{"key":"9279_CR24","series-title":"Optimization","first-page":"283","volume-title":"A method for nonlinear constraints in minimization problems","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.\u00a0283\u2013298. Academic Press, New York (1969)"},{"key":"9279_CR25","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/BF01580138","volume":"5","author":"R.T. Rockafellar","year":"1973","unstructured":"Rockafellar, R.T.: A dual approach to solving nonlinear programming problems by unconstrained optimization. Math. Program. 5, 354\u2013373 (1973)","journal-title":"Math. Program."},{"key":"9279_CR26","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF00934777","volume":"12","author":"R.T. Rockafellar","year":"1973","unstructured":"Rockafellar, R.T.: The multiplier method of Hestenes and Powell applied to convex programming. J.\u00a0Optim. Theory Appl. 12, 555\u2013562 (1973)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9279_CR27","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 12, 268\u2013285 (1974)","journal-title":"SIAM J. Control"},{"key":"9279_CR28","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1287\/moor.1070.0300","volume":"33","author":"D.F. Sun","year":"2008","unstructured":"Sun, D.F., Sun, J.: L\u00f6wner\u2019s operator and spectral functions in Euclidean Jordan algebras. Math. Oper. Res. 33 421\u2013445 (2008)","journal-title":"Math. Oper. Res."},{"key":"9279_CR29","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s10957-006-9078-8","volume":"129","author":"J. Sun","year":"2006","unstructured":"Sun, J., Zhang, L.W., Wu, Y.: Properties of the augmented Lagrangian in nonlinear semidefinite optimization. J. Optim. Theory Appl. 129, 437\u2013456 (2006)","journal-title":"J. Optim. Theory Appl."},{"key":"9279_CR30","author":"D.F. Sun","year":"2008","unstructured":"Sun, D.F., Sun, J., Zhang, L.W.: The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming. Math. Program. (2008) doi: 10.1007\/s10107-007-0105-9","journal-title":"Math. Program."},{"key":"9279_CR31","volume-title":"On the Solution of Nonlinear Semidefinite Programs by Augmented Lagrangian Methods","author":"M. Stingl","year":"2006","unstructured":"Stingl, M.: On the Solution of Nonlinear Semidefinite Programs by Augmented Lagrangian Methods. Shaker, Aachen (2006). Dissertation"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9279-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-009-9279-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9279-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T13:48:49Z","timestamp":1710510529000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-009-9279-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,28]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["9279"],"URL":"https:\/\/doi.org\/10.1007\/s10589-009-9279-9","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,28]]}}}