{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T16:43:47Z","timestamp":1783788227240,"version":"3.55.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,1,20]],"date-time":"2007-01-20T00:00:00Z","timestamp":1169251200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2007,7,19]]},"DOI":"10.1007\/s10107-006-0088-y","type":"journal-article","created":{"date-parts":[[2007,1,19]],"date-time":"2007-01-19T15:13:08Z","timestamp":1169219588000},"page":"221-254","source":"Crossref","is-referenced-by-count":90,"title":["An inexact primal\u2013dual path following algorithm for convex quadratic SDP"],"prefix":"10.1007","volume":"112","author":[{"given":"Kim-Chuan","family":"Toh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,1,20]]},"reference":[{"key":"88_CR1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1023\/A:1008655427845","volume":"12","author":"A.Y. Alfakih","year":"1999","unstructured":"Alfakih A.Y., Khandani A. and Wolkowicz H. (1999). Solving Euclidean distance matrix completion problems via semidefinite programming. Comput. Optim. Appl. 12: 13\u201330","journal-title":"Comput. Optim. Appl."},{"key":"88_CR2","first-page":"111","volume":"77","author":"F. Alizadeh","year":"1997","unstructured":"Alizadeh F., Haeberly J.-P.A. and Overton M.L. (1997). Complementarity and nondegeneracy in semidefinite programming.. Math. Program. 77: 111\u2013128","journal-title":"Math. Program."},{"key":"88_CR3","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1137\/S1052623496304700","volume":"8","author":"F. Alizadeh","year":"1998","unstructured":"Alizadeh F., Haeberly J.-P.A. and Overton M.L. (1998). Primal\u2013dual interior-point methods for semidefinite programming: convergence results, stability and numerical results. SIAM J. Optim. 8: 746\u2013768","journal-title":"SIAM J. Optim."},{"key":"88_CR4","unstructured":"Anjos, M.F., Higham, N.J., Takouda, P.L., Wolkowicz, H.: A semidefinite programming approach for the nearest correlation matrix problem. Research Report, Department of Combinatorics and Optimization, University of Waterloo (2003)"},{"key":"88_CR5","doi-asserted-by":"crossref","unstructured":"Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 1\u2013137 (2005)","DOI":"10.1017\/S0962492904000212"},{"key":"88_CR6","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s00211-006-0679-9","volume":"103","author":"M. Benzi","year":"2006","unstructured":"Benzi M. and Simoncini V. (2006). On the eigenvalues of a class of saddle point matrices. Numer. Math. 103: 173\u2013196","journal-title":"Numer. Math."},{"key":"88_CR7","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/B:COAP.0000026882.34332.1b","volume":"28","author":"L. Bergamaschi","year":"2004","unstructured":"Bergamaschi L., Gondzio J. and Zilli G. (2004). Preconditioning indefinite systems in interior point methods for optimization. Comput. Optim. Appl. 28: 149\u2013171","journal-title":"Comput. Optim. Appl."},{"key":"88_CR8","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1093\/nar\/28.1.235","volume":"28","author":"H.M. Berman","year":"2000","unstructured":"Berman H.M., Westbrook J., Feng Z., Gilliland G., Bhat T.N., Weissig H., Shindyalov I.N. and Bourne P.E. (2000). The protein data bank. Nucl. Acids Res. 28: 235\u2013242","journal-title":"Nucl. Acids Res."},{"key":"88_CR9","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1007\/BF01446925","volume":"287","author":"R. Bhatia","year":"1990","unstructured":"Bhatia R. and Kittaneh F. (1990). Norm inequalities for partitioned operators and an application. Math. Ann. 287: 719\u2013726","journal-title":"Math. Ann."},{"key":"88_CR10","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s101070100279","volume":"93","author":"S. Burer","year":"2002","unstructured":"Burer S., Monteiro R.D.C. and Zhang Y. (2002). Solving a class of semidefinite programs via nonlinear programming. Math. Program. 93: 97\u2013122","journal-title":"Math. Program."},{"key":"88_CR11","doi-asserted-by":"crossref","unstructured":"Freund, R.W., Nachtigal, N.M.: A new Krylov-subspace method for symmetric indefinite linear systems. In: Ames W.F. (ed.) Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, Atlanta, USA, pp. 1253\u20131256 (1994)","DOI":"10.2172\/10190810"},{"key":"88_CR12","first-page":"235","volume":"79","author":"K. Fujisawa","year":"1997","unstructured":"Fujisawa K., Kojima M. and Nakata K. (1997). Exploiting sparsity in primal-dual interior-point method for semidefinite programming. Math. Program. 79: 235\u2013253","journal-title":"Math. Program."},{"key":"88_CR13","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/10556780410001727718","volume":"20","author":"M. Halicka","year":"2005","unstructured":"Halicka M., Roos C. and Klerk E. (2005). Limiting behaviour of the central path in semidefinite optimization. Optim. Methods Softw. 20: 99\u2013113","journal-title":"Optim. Methods Softw."},{"key":"88_CR14","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1093\/imanum\/22.3.329","volume":"22","author":"N.J. Higham","year":"2002","unstructured":"Higham N.J. (2002). Computing the nearest correlation matrix\u2014a problem from finance. IMA J. Numer. Anal. 22: 329\u2013343","journal-title":"IMA J. Numer. Anal."},{"key":"88_CR15","unstructured":"Horn, R., Johnson, C. Matrix Analysis. Cambridge University Press, Cambridge (1998)"},{"key":"88_CR16","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1137\/S0895479899351805","volume":"21","author":"C. Keller","year":"2000","unstructured":"Keller C., Gould N.I.M. and Wathen A.J. (2000). Constraint preconditioning for indefinite linear systems. Matrix Anal. Appl. 21: 1300\u20131317","journal-title":"Matrix Anal. Appl."},{"key":"88_CR17","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1137\/S1052623494269035","volume":"7","author":"M. Kojima","year":"1997","unstructured":"Kojima M., Shindoh S. and Hara S. (1997). Interior-point methods for the monotone linear complementarity problem in symmetric matrices. SIAM J. Optim. 7: 86\u2013125","journal-title":"SIAM J. Optim."},{"key":"88_CR18","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1109\/TRO.2004.832794","volume":"20","author":"N. Krislock","year":"2004","unstructured":"Krislock N., Lang J., Varah J., Pai D.K. and Seidel H.-P. (2004). Local compliance estimation via positive semidefinite constrained least sqaures. IEEE Trans. Robot. 20: 1007\u20131011","journal-title":"IEEE Trans. Robot."},{"key":"88_CR19","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1002\/nla.344","volume":"11","author":"A.N. Langville","year":"2004","unstructured":"Langville A.N. and Stewart W.J. (2004). A Kronecker product approximate preconditioner for SANs. Numer. Linear Algebra Appl. 11: 723\u2013752","journal-title":"Numer. Linear Algebra Appl."},{"key":"88_CR20","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1137\/S1052623496299187","volume":"8","author":"Z.-Q. Luo","year":"1998","unstructured":"Luo Z.-Q., Sturm J.F. and Zhang S. (1998). Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming. SIAM J. Optim. 8: 59\u201381","journal-title":"SIAM J. Optim."},{"key":"88_CR21","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1137\/S0895479802413856","volume":"26","author":"J. Malick","year":"2004","unstructured":"Malick J. (2004). A dual approach to semidefinite least-squares problems. SIAM J. Matrix Anal. Appl. 26: 272\u2013284","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"12","key":"88_CR22","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/10556789908805749","volume":"11","author":"R.D.C. Monteiro","year":"1999","unstructured":"Monteiro R.D.C. and Zanj\u00e1como P.R. (1999). Implementation of primal-dual methods for semidefinite programming based on Monteiro and Tsuchiya Newton directions and their variants.. Optim. Methods Softw. 11(12): 91\u2013140","journal-title":"Optim. Methods Softw."},{"key":"88_CR23","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1023\/A:1012994820412","volume":"103","author":"J.W. Nie","year":"2001","unstructured":"Nie J.W. and Yuan Y.X. (2001). A predictor-corrector algorithm for QSDP combining Dikin-type and Newton centering steps. Ann. Oper. Res. 103: 115\u2013133","journal-title":"Ann. Oper. Res."},{"key":"88_CR24","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1002\/nme.500","volume":"55","author":"K.K. Phoon","year":"2002","unstructured":"Phoon K.K., Toh K.C., Chan S.H. and Lee F.H. (2002). An efficient diagonal preconditioner for finite element solution of Biot\u2019s consolidation equations. Int. J. Numer. Methods in Eng. 55: 377\u2013400","journal-title":"Int. J. Numer. Methods in Eng."},{"key":"88_CR25","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1137\/050624509","volume":"28","author":"H. Qi","year":"2006","unstructured":"Qi H. and Sun D. (2006). A quadratically convergent Newton method for computing the nearest correlation matrix. SIAM J. Matrix Anal. Appl. 28: 360\u2013385","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"88_CR26","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y. Saad","year":"1996","unstructured":"Saad Y. (1996). Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston"},{"key":"88_CR27","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1137\/S105262349630060X","volume":"8","author":"M.J. Todd","year":"1998","unstructured":"Todd M.J., Toh K.C. and T\u00fct\u00fcnc\u00fc R.H. (1998). On the Nesterov-Todd direction in semidefinite programming.. SIAM J. Optim. 8: 769\u2013796","journal-title":"SIAM J. Optim."},{"key":"88_CR28","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1002\/nme.982","volume":"60","author":"K.C. Toh","year":"2004","unstructured":"Toh K.C., Phoon K.K. and Chan S.H. (2004). Block preconditioners for symmetric indefinite linear systems. Int. J. Numer. Methods Eng. 60: 1361\u20131381","journal-title":"Int. J. Numer. Methods Eng."},{"key":"88_CR29","unstructured":"Toh, K.C., T\u00fct\u00fcnc\u00fc, R.H., Todd, M.J.: Inexact primal\u2013dual path-following algorithms for a special class of convex quadratic SDP and related problems. Pacific J. Optim. (in press)"},{"key":"88_CR30","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0377-0427(00)00393-9","volume":"123","author":"C.F. Van Loan","year":"2000","unstructured":"Van Loan C.F. (2000). The ubiquitous Kronecker product. J. Comput. Appl. Math. 123: 85\u2013100","journal-title":"J. Comput. Appl. Math."},{"key":"88_CR31","unstructured":"Wathen, A.J., Fischer, B., Silvester, D.J.: The convergence of iterative solution methods for symmetric and indefinite linear systems. In: Griffiths, D.F., Watson, G.A., (eds.) Numerical Analysis 1997. Addison Wesley Longman, Harlow, pp. 230\u2013243 (1997)"},{"key":"88_CR32","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10107-003-0431-5","volume":"99","author":"G.L. Zhou","year":"2004","unstructured":"Zhou G.L. and Toh K.C. (2004). Polynomiality of an inexact infeasible interior point algorithm for semidefinite programming. Math. Program. 99: 261\u2013282","journal-title":"Math. Program."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-006-0088-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-006-0088-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-006-0088-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T09:50:02Z","timestamp":1559123402000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-006-0088-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,20]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,7,19]]}},"alternative-id":["88"],"URL":"https:\/\/doi.org\/10.1007\/s10107-006-0088-y","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1,20]]}}}