{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T21:11:26Z","timestamp":1719177086737},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,5,29]],"date-time":"2013-05-29T00:00:00Z","timestamp":1369785600000},"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":[[2013,12]]},"DOI":"10.1007\/s10589-013-9568-1","type":"journal-article","created":{"date-parts":[[2013,5,28]],"date-time":"2013-05-28T15:31:07Z","timestamp":1369755067000},"page":"531-558","source":"Crossref","is-referenced-by-count":19,"title":["Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming"],"prefix":"10.1007","volume":"56","author":[{"given":"Huixian","family":"Wu","sequence":"first","affiliation":[]},{"given":"Hezhi","family":"Luo","sequence":"additional","affiliation":[]},{"given":"Xiaodong","family":"Ding","sequence":"additional","affiliation":[]},{"given":"Guanting","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,5,29]]},"reference":[{"key":"9568_CR1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10107-006-0077-1","volume":"111","author":"R. Andreani","year":"2008","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Program. 111, 5\u201332 (2008)","journal-title":"Math. Program."},{"key":"9568_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":"9568_CR3","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":"9568_CR4","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1023\/A:1010091831812","volume":"1","author":"A. Ben-Tal","year":"2000","unstructured":"Ben-Tal, A., Jarre, F., Kocvara, M., Nemirovski, A., Zowe, J.: Optimal design of trusses under a nonconvex global buckling constraints. Optim. Eng. 1, 189\u2013213 (2000)","journal-title":"Optim. Eng."},{"key":"9568_CR5","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":"9568_CR6","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":"9568_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"J.F. Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)"},{"key":"9568_CR8","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1137\/070681235","volume":"19","author":"Z.X. Chan","year":"2008","unstructured":"Chan, Z.X., Sun, D.: Constraint nondegeneracy, strong regularity and nonsingularity in semidefinite programming. SIAM J. Optim. 19, 370\u2013396 (2008)","journal-title":"SIAM J. Optim."},{"key":"9568_CR9","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1137\/0806023","volume":"6","author":"T.F. Coleman","year":"1996","unstructured":"Coleman, T.F., Li, Y., Kaya, C.Y.: An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418\u2013445 (1996)","journal-title":"SIAM J. Optim."},{"key":"9568_CR10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01582221","volume":"67","author":"T.F. Coleman","year":"1994","unstructured":"Coleman, T.F., Li, Y.: On the convergence of reflective Newton methods for largescale nonlinear minimization subject to bounds. Math. Program. 67, 189\u2013224 (1994)","journal-title":"Math. Program."},{"key":"9568_CR11","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1137\/S1052623493251463","volume":"6","author":"A.R. Conn","year":"1996","unstructured":"Conn, A.R., Gould, N.I.M., Sartenaer, A., Toint, P.L.: Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints. SIAM J. Optim. 6, 674\u2013703 (1996)","journal-title":"SIAM J. Optim."},{"key":"9568_CR12","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1137\/0728030","volume":"28","author":"A.R. Conn","year":"1991","unstructured":"Conn, A.R., Gould, N.I.M., Toint, P.L.: A\u00a0globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28, 545\u2013572 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"9568_CR13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1137\/S1052623402417298","volume":"15","author":"R. Correa","year":"2004","unstructured":"Correa, R., Ram\u00edrez, C.H.: A\u00a0global algorithm for solving nonlinear semidefinite programming. SIAM J.\u00a0Optim. 15, 303\u2013318 (2004)","journal-title":"SIAM J.\u00a0Optim."},{"key":"9568_CR14","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s10957-004-5720-5","volume":"123","author":"M.A. Diniz-Ehrhardt","year":"2004","unstructured":"Diniz-Ehrhardt, M.A., Gomes-Ruggiero, M.A., Mart\u0131nez, J.M., Santos, S.A.: Augmented Lagrangian algorithms based on the spectral projected gradient method for solving nonlinear programming problems. J.\u00a0Optim. Theory Appl. 123, 497\u2013517 (2004)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9568_CR15","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1080\/00207170010010605","volume":"74","author":"B. Fares","year":"2001","unstructured":"Fares, B., Apkarian, P., Noll, D.: An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory. Int. J. Control 74, 348\u2013360 (2001)","journal-title":"Int. J. Control"},{"key":"9568_CR16","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1137\/S0363012900373483","volume":"40","author":"B. Fares","year":"2002","unstructured":"Fares, B., Noll, D., Apkarian, P.: Robust control via sequential semidefinite programming. SIAM J. Control Optim. 40, 1791\u20131820 (2002)","journal-title":"SIAM J. Control Optim."},{"key":"9568_CR17","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/PL00011370","volume":"88","author":"A. Forsgren","year":"2000","unstructured":"Forsgren, A.: Optimality conditions for nonconvex semidefinite programming. Math. Program. 88, 105\u2013128 (2000)","journal-title":"Math. Program."},{"key":"9568_CR18","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1007\/s10114-005-0702-6","volume":"22","author":"X.X. Huang","year":"2006","unstructured":"Huang, X.X., Teo, K.L., Yang, X.Q.: Approximate augmented Lagrangian functions and nonlinear semidefinite programs. Acta Math. Sin. Engl. Ser. 22, 1283\u20131296 (2006)","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"9568_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10957-006-9055-2","volume":"132","author":"X.X. Huang","year":"2007","unstructured":"Huang, X.X., Teo, K.L., Yang, X.Q.: Lower-order penalization to nonlinear semidefinite programming. J.\u00a0Optim. Theory Appl. 132, 1\u201320 (2007)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9568_CR20","series-title":"Nonconvex Optimization and Its Applications","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/0-387-24276-7_32","volume-title":"Variational Analysis and Applications","author":"X.X. Huang","year":"2005","unstructured":"Huang, X.X., Yang, X.Q., Teo, K.L.: Augmented Lagrangian and nonlinear semidefinite programs. In: Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol. 79, pp. 513\u2013529 (2005)"},{"key":"9568_CR21","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1023\/A:1011562523132","volume":"1","author":"F. Jarre","year":"2000","unstructured":"Jarre, F.: An interior point method for semidefinite programs. Optim. Eng. 1, 347\u2013372 (2000)","journal-title":"Optim. Eng."},{"key":"9568_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S1052623401390525","volume":"13","author":"C. Kanzow","year":"2002","unstructured":"Kanzow, C., Nagel, C.: Semidefinite programs: new search directions, smoothing-type methods, and numerical results. SIAM J. Optim. 13, 1\u201323 (2002)","journal-title":"SIAM J. Optim."},{"key":"9568_CR23","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1137\/S1052623498339727","volume":"12","author":"R.M. Lewis","year":"2002","unstructured":"Lewis, R.M., Torczon, V.: A\u00a0globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM J. Optim. 12, 1075\u20131089 (2002)","journal-title":"SIAM J. Optim."},{"key":"9568_CR24","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1007\/s10898-011-9779-x","volume":"54","author":"H.Z. Luo","year":"2012","unstructured":"Luo, H.Z., Wu, H.X., Chen, G.T.: On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming. J. Glob. Optim. 54, 599\u2013618 (2012)","journal-title":"J. Glob. Optim."},{"key":"9568_CR25","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s10957-009-9598-0","volume":"144","author":"H.Z. Luo","year":"2010","unstructured":"Luo, H.Z., Mastroeni, G., Wu, H.X.: Separation approach for augmented Lagrangians in constrained nonconvex optimization. J.\u00a0Optim. Theory Appl. 144, 275\u2013290 (2010)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9568_CR26","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1137\/060667086","volume":"18","author":"H.Z. Luo","year":"2007","unstructured":"Luo, H.Z., Sun, X.L., Li, D.: On the convergence of augmented Lagrangian methods for constrained global optimization. SIAM J. Optim. 18, 1209\u20131230 (2007)","journal-title":"SIAM J. Optim."},{"key":"9568_CR27","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1080\/10556780802124648","volume":"23","author":"H.Z. Luo","year":"2008","unstructured":"Luo, H.Z., Sun, X.L., Wu, H.X.: Convergence properties of augmented Lagrangian methods for constrained global optimization. Optim. Methods Softw. 23, 763\u2013778 (2008)","journal-title":"Optim. Methods Softw."},{"key":"9568_CR28","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s10957-009-9642-0","volume":"145","author":"H.Z. Luo","year":"2010","unstructured":"Luo, H.Z., Sun, X.L., Xu, Y.F.: Convergence properties of modified and partially-augmented Lagrangian methods for mathematical programming with complementarity constraints. J.\u00a0Optim. Theory Appl. 145, 489\u2013506 (2010)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9568_CR29","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s10898-009-9419-x","volume":"46","author":"H.Z. Luo","year":"2010","unstructured":"Luo, H.Z., Sun, X.L., Xu, Y.F., Wu, H.X.: On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints. J. Glob. Optim. 46, 217\u2013232 (2010)","journal-title":"J. Glob. Optim."},{"key":"9568_CR30","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/10556780008805787","volume":"13","author":"L. Mosheyev","year":"2000","unstructured":"Mosheyev, L., Zibulevsky, M.: Penalty\/barrier multiplier algorithm for semidefinite programming. Optim. Methods Softw. 13, 235\u2013261 (2000)","journal-title":"Optim. Methods Softw."},{"key":"9568_CR31","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":"9568_CR32","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1080\/10556780701223970","volume":"22","author":"D. Noll","year":"2007","unstructured":"Noll, D.: Local convergence of an augmented Lagrangian method for matrix inequality constrained programming. Optim. Methods Softw. 22, 777\u2013802 (2007)","journal-title":"Optim. Methods Softw."},{"key":"9568_CR33","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1287\/moor.1080.0315","volume":"34","author":"H.D. Qi","year":"2009","unstructured":"Qi, H.D.: Local duality of nonlinear semidefinite programming. Math. Oper. Res. 34, 124\u2013141 (2009)","journal-title":"Math. Oper. Res."},{"key":"9568_CR34","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":"9568_CR35","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":"9568_CR36","first-page":"301","volume":"77","author":"A. Shapiro","year":"1997","unstructured":"Shapiro, A.: First and second order analysis of nonlinear semidefinite programs. Math. Program., Ser.\u00a0B 77, 301\u2013320 (1997)","journal-title":"Math. Program., Ser.\u00a0B"},{"key":"9568_CR37","unstructured":"Stingl, M.: On the solution of nonlinear semidefinite programs by augmented Lagrangian methods. PhD thesis, Institute of Applied Mathematics, University Erlangen-Nurnberg (2005)"},{"key":"9568_CR38","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1287\/moor.1060.0195","volume":"31","author":"D. Sun","year":"2006","unstructured":"Sun, D.: The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math. Oper. Res. 31, 761\u2013776 (2006)","journal-title":"Math. Oper. Res."},{"key":"9568_CR39","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s10107-007-0105-9","volume":"114","author":"D. Sun","year":"2008","unstructured":"Sun, D., Sun, J., Zhang, L.W.: The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming. Math. Program. 114, 349\u2013391 (2008)","journal-title":"Math. Program."},{"key":"9568_CR40","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.\u00a0Optim. Theory Appl. 129, 437\u2013456 (2006)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9568_CR41","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1017\/S0962492901000071","volume":"10","author":"M. Todd","year":"2001","unstructured":"Todd, M.: Semidefinite optimization. Acta Numer. 10, 515\u2013560 (2001)","journal-title":"Acta Numer."},{"key":"9568_CR42","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L. Vandenberghe","year":"1996","unstructured":"Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Rev. 38, 49\u201395 (1996)","journal-title":"SIAM Rev."},{"key":"9568_CR43","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1007\/s10898-011-9731-0","volume":"53","author":"H.X. Wu","year":"2012","unstructured":"Wu, H.X., Luo, H.Z.: Saddle points of general augmented Lagrangians for constrained nonconvex optimization. J. Glob. Optim. 53, 683\u2013697 (2012)","journal-title":"J. Glob. Optim."},{"key":"9568_CR44","first-page":"296","volume":"203","author":"H. Yamashita","year":"2007","unstructured":"Yamashita, H., Yabe, H.: A\u00a0primal-dual interior point method for nonlinear semidefinite programming. Inst. Stat. Math. Cooper. Res. Report 203, 296\u2013317 (2007)","journal-title":"Inst. Stat. Math. Cooper. Res. Report"},{"key":"9568_CR45","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s10107-011-0449-z","volume":"135","author":"H. Yamashita","year":"2012","unstructured":"Yamashita, H., Yabe, H., Harada, K.: A\u00a0primal-dual interior point method for nonlinear semidefinite programming. Math. Program. 135, 89\u2013121 (2012)","journal-title":"Math. Program."},{"key":"9568_CR46","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032701","volume-title":"Interior Point Algorithms: Theory and Analysis","author":"Y. Ye","year":"1997","unstructured":"Ye, Y.: Interior Point Algorithms: Theory and Analysis. Wiley, New York (1997)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9568-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-013-9568-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9568-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T18:37:34Z","timestamp":1559241454000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-013-9568-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,29]]},"references-count":46,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["9568"],"URL":"https:\/\/doi.org\/10.1007\/s10589-013-9568-1","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,29]]}}}