{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T04:48:38Z","timestamp":1766983718806},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,11,19]],"date-time":"2010-11-19T00:00:00Z","timestamp":1290124800000},"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":[[2011,10]]},"DOI":"10.1007\/s10589-010-9374-y","type":"journal-article","created":{"date-parts":[[2010,11,18]],"date-time":"2010-11-18T16:29:52Z","timestamp":1290097792000},"page":"327-349","source":"Crossref","is-referenced-by-count":5,"title":["Block relaxation and majorization methods for\u00a0the\u00a0nearest correlation matrix with factor structure"],"prefix":"10.1007","volume":"50","author":[{"given":"Qingna","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Houduo","family":"Qi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naihua","family":"Xiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,11,19]]},"reference":[{"key":"9374_CR1","series-title":"Applied and Numerical Harmonic Analysis","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/978-0-8176-4545-8_14","volume-title":"Advances in Mathematical Finance","author":"H. Albrecher","year":"2007","unstructured":"Albrecher, H., Ladoucette, S., Schoutens, W.: A generic one-factor L\u00e9vy model for pricing synthetic CDOs. In: Fu, M.C., Jarrow, R.A., Yen, J.-Y.J., Elliott, R.J. (eds.) Advances in Mathematical Finance. Applied and Numerical Harmonic Analysis, pp. 259\u2013277. Birkha\u00fcser, Boston (2007)"},{"key":"9374_CR2","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. Control Optim. 10, 1196\u20131211 (2000)","journal-title":"SIAM J. Control Optim."},{"key":"9374_CR3","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1145\/502800.502803","volume":"27","author":"E.G. Birgin","year":"2001","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Algorithm 813: SPG-Software for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340\u2013349 (2001)","journal-title":"ACM Trans. Math. Softw."},{"key":"9374_CR4","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1093\/imanum\/drn085","volume":"94","author":"R. Borsdorf","year":"2010","unstructured":"Borsdorf, R., Higham, N.J.: A preconditioned Newton algorithm for the nearest correlation matrix. IMA J. Numer. Anal. 94, 94\u2013107 (2010)","journal-title":"IMA J. Numer. Anal."},{"key":"9374_CR5","doi-asserted-by":"crossref","first-page":"2603","DOI":"10.1137\/090776718","volume":"31","author":"R. Borsdorf","year":"2010","unstructured":"Borsdorf, R., Higham, N.J., Raydan, M.: Computing a nearest correlation matrix with factor structure. SIAM J. Matrix Anal. Appl. 31, 2603\u20132622 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9374_CR6","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1137\/040609902","volume":"27","author":"S. Boyd","year":"2005","unstructured":"Boyd, S., Xiao, L.: Least-squares covariance matrix adjustment. SIAM J. Matrix Anal. Appl. 27, 532\u2013546 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9374_CR7","volume-title":"Recent Advantages in Statistics","author":"J. Leeuw de","year":"1977","unstructured":"de Leeuw, J.: Application of convex analysis to multidimensional scaling. In: van Cutsem, B., et al. (eds.) Recent Advantages in Statistics. North Holland, Amsterdam (1977)"},{"key":"9374_CR8","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1007\/978-3-642-46808-7_28","volume-title":"Information Systems and Data Analysis","author":"J. Leeuw de","year":"1994","unstructured":"de Leeuw, J.: Block relaxation algorithms in statistics. In: Bock, H.H., et al. (eds.) Information Systems and Data Analysis, pp. 308\u2013325. Springer, Berlin (1994)"},{"key":"9374_CR9","volume-title":"Common Principle Components and Related Multivariate Models","author":"B. Flury","year":"1988","unstructured":"Flury, B.: Common Principle Components and Related Multivariate Models. Wiley, New York (1988)"},{"key":"9374_CR10","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1137\/080727075","volume":"31","author":"Y. Gao","year":"2009","unstructured":"Gao, Y., Sun, D.F.: Calibrating least squares covariance matrix problems with equality and inequality constraints. SIAM J. Matrix Anal. Appl. 31, 1432\u20131457 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9374_CR11","volume-title":"Matrix Optimization","author":"G.H. Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Optimization, 3rd edn. John Hopkins University Press, Baltimore (1996)","edition":"3"},{"key":"9374_CR12","first-page":"150","volume":"41","author":"H.A.L. Kiers","year":"2002","unstructured":"Kiers, H.A.L.: Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems. Comput. Stat. Data Anal. 41, 150\u2013170 (2002)","journal-title":"Comput. Stat. Data Anal."},{"key":"9374_CR13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1093\/oso\/9780198522850.003.0008","volume-title":"Recent Advances in Descriptive Multivariate Analysis","author":"W.J. Heiser","year":"1995","unstructured":"Heiser, W.J.: Convergent computation by iterative majorization: theory and applications in multidimensional data analysis. In: Krzanowski, W.J. (eds.) Recent Advances in Descriptive Multivariate Analysis, pp. 157\u2013189. Oxford University Press, Oxford (1995)"},{"key":"9374_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.: Computing the nearest correlation matrix\u2014a problem from finance. IMA J. Numer. Anal. 22, 329\u2013343 (2002)","journal-title":"IMA J. Numer. Anal."},{"key":"9374_CR15","doi-asserted-by":"crossref","first-page":"46","DOI":"10.3905\/jfi.2000.319268","volume":"10","author":"J.C. Hull","year":"2000","unstructured":"Hull, J.C., White, A.: Forward rate volatilities, swap rate volatilities, and the implementation of the LIBOR market model. J. Fixed Income 10, 46\u201362 (2000)","journal-title":"J. Fixed Income"},{"key":"9374_CR16","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1137\/S0895479802413856","volume":"26","author":"J. Malick","year":"2004","unstructured":"Malick, J.: A dual approach to semidefinite least-squares problems. SIAM J. Matrix Anal. Appl. 26, 272\u2013284 (2004)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9374_CR17","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/0904038","volume":"4","author":"J.J. Mor\u00e9","year":"1983","unstructured":"Mor\u00e9, J.J., Sorensen, D.C.: Computing a trust region step. SIAM J. Sci. Comput. 4, 553\u2013572 (1983)","journal-title":"SIAM J. Sci. Comput."},{"key":"9374_CR18","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, Berlin (1999)"},{"key":"9374_CR19","series-title":"ERIM PhD Series in Management","volume-title":"Pricing Models for Bermudan-Style Interest Rate Derivatives","author":"R. Pietersz","year":"2005","unstructured":"Pietersz, R.: Pricing Models for Bermudan-Style Interest Rate Derivatives. ERIM PhD Series in Management. Erasmus University, Rotterdam (2005)"},{"key":"9374_CR20","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1080\/14697680400016182","volume":"4","author":"R. Pietersz","year":"2004","unstructured":"Pietersz, R., Grubi\u0161i\u0107, I.: Rank reduction of correlation matrices by majorization. Quant. Finance 4, 649\u2013662 (2004)","journal-title":"Quant. Finance"},{"key":"9374_CR21","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1137\/050624509","volume":"28","author":"H.D. Qi","year":"2006","unstructured":"Qi, H.D., Sun, D.F.: A quadratically convergent Newton method for computing the nearest correlation matrix. SIAM J. Matrix Anal. Appl. 28, 360\u2013385 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"9374_CR22","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1145\/1326548.1326553","volume":"34","author":"M. Rojas","year":"2008","unstructured":"Rojas, M., Santos, S.A., Sorensen, D.C.: Algorithm 873: LSTRS: MATLAB software for large-scale trust region subproblems and regularization. ACM Trans. Math. Softw. 34(2), 11 (2008)","journal-title":"ACM Trans. Math. Softw."},{"key":"9374_CR23","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.laa.2009.01.004","volume":"431","author":"P. Sonneveld","year":"2009","unstructured":"Sonneveld, P., van Kan, J.J.I.M., Huang, X., Oosterlee, C.W.: Nonnegative matrix factorization of a correlation matrix. Linear Algebra Appl. 431, 334\u2013349 (2009)","journal-title":"Linear Algebra Appl."},{"key":"9374_CR24","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1137\/0720042","volume":"20","author":"T. Steihaug","year":"1983","unstructured":"Steihaug, T.: The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626\u2013637 (1983)","journal-title":"SIAM J. Numer. Anal."},{"key":"9374_CR25","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s10107-006-0088-y","volume":"112","author":"K.C. Toh","year":"2008","unstructured":"Toh, K.C.: An inexact path-following algorithm for convex quadratic SDP. Math. Program. 112, 221\u2013254 (2008)","journal-title":"Math. Program."},{"key":"9374_CR26","first-page":"135","volume":"3","author":"K.C. Toh","year":"2007","unstructured":"Toh, K.C., T\u00fct\u00fcnc\u00fc, R.H., Todd, M.J.: Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Pac. J. Optim. 3, 135\u2013164 (2007)","journal-title":"Pac. J. Optim."},{"issue":"3","key":"9374_CR27","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s101070050012","volume":"87","author":"Y. Yuan","year":"2000","unstructured":"Yuan, Y.: On the truncated conjugate gradient method. Math. Program., Ser. A 87(3), 561\u2013573 (2000)","journal-title":"Math. Program., Ser. A"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-010-9374-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-010-9374-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-010-9374-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T09:37:14Z","timestamp":1711964234000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-010-9374-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,19]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["9374"],"URL":"https:\/\/doi.org\/10.1007\/s10589-010-9374-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,19]]}}}