{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T00:53:24Z","timestamp":1774745604982,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,9,27]],"date-time":"2020-09-27T00:00:00Z","timestamp":1601164800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,27]],"date-time":"2020-09-27T00:00:00Z","timestamp":1601164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s10589-020-00228-5","type":"journal-article","created":{"date-parts":[[2020,9,27]],"date-time":"2020-09-27T18:02:37Z","timestamp":1601229757000},"page":"1-42","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An accelerated active-set algorithm for a quadratic semidefinite program with general constraints"],"prefix":"10.1007","volume":"78","author":[{"given":"Chungen","family":"Shen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunlong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjuan","family":"Xue","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei-Hong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,9,27]]},"reference":[{"key":"228_CR1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two point step size gradient methods. IMA J. Numer. Anal. 8, 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"228_CR2","doi-asserted-by":"publisher","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":"228_CR3","doi-asserted-by":"publisher","first-page":"960","DOI":"10.1137\/S1052623400380584","volume":"13","author":"X Chen","year":"2003","unstructured":"Chen, X., Qi, H., Tseng, P.: Analysis of nonsmooth symmetric-matrix-valued functions with applications to semidefinite complementarity problems. SIAM J. Optim. 13, 960\u2013985 (2003)","journal-title":"SIAM J. Optim."},{"key":"228_CR4","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)"},{"key":"228_CR5","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1080\/02331930310001611547","volume":"52","author":"YH Dai","year":"2003","unstructured":"Dai, Y.H.: Alternate step gradient method. Optimization 52, 395\u2013415 (2003)","journal-title":"Optimization"},{"issue":"3","key":"228_CR6","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0167-6377(94)00059-F","volume":"17","author":"F Facchinei","year":"1995","unstructured":"Facchinei, F.: Minimization of SC$$^1$$ functions and the Maratos effect. Oper. Res. Lett. 17(3), 131\u2013137 (1995)","journal-title":"Oper. Res. Lett."},{"issue":"1","key":"228_CR7","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1137\/S1052623496305882","volume":"9","author":"F Facchinei","year":"1998","unstructured":"Facchinei, F., Fischer, A., Kanzow, C.: On the accurate identification of active constraints. SIAM J. Optim. 9(1), 14\u201332 (1998)","journal-title":"SIAM J. Optim."},{"key":"228_CR8","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0168-2024(08)70034-1","volume-title":"Augmented Lagrangian Methods: Application to the Numerical Solution of Boundary-Value Problems","author":"D Gabay","year":"1983","unstructured":"Gabay, D.: Application of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrangian Methods: Application to the Numerical Solution of Boundary-Value Problems, pp. 299\u2013331. North-Holland, Amsterdam (1983)"},{"key":"228_CR9","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","volume":"2","author":"D Gabay","year":"1976","unstructured":"Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"228_CR10","doi-asserted-by":"publisher","first-page":"1432","DOI":"10.1137\/080727075","volume":"31","author":"Y Gao","year":"2009","unstructured":"Gao, Y., Sun, D.F.: Calibrating least squares semidefinite programming with equality and inequality constraints. SIAM J. Matrix Anal. Appl. 31, 1432\u20131457 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"02","key":"228_CR11","doi-asserted-by":"publisher","first-page":"1750018","DOI":"10.1142\/S0219477517500183","volume":"16","author":"RQ Han","year":"2017","unstructured":"Han, R.Q., Xie, W.J., Xiong, X.: Market correlation structure changes around the great crash: a random matrix theory analysis of the Chinese stock market. Fluct. Noise Lett. 16(02), 1750018 (2017)","journal-title":"Fluct. Noise Lett."},{"key":"228_CR12","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1137\/090768813","volume":"32","author":"BS He","year":"2011","unstructured":"He, B.S., Xu, M.H., Yuan, X.M.: Solving large-scale least squares covariance matrix problems by alternating direction methods. SIAM J. Matrix Anal. Appl. 32, 136\u2013152 (2011)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"228_CR13","doi-asserted-by":"publisher","first-page":"7","DOI":"10.3905\/jod.1998.408008","volume":"6","author":"PH Kupiec","year":"1998","unstructured":"Kupiec, P.H.: Stress testing in a value-at-risk framework. J. Deriv. 6, 7\u201324 (1998)","journal-title":"J. Deriv."},{"key":"228_CR14","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1137\/1.9781611970920","volume-title":"Iterative Methods for Optimization","author":"CT Kelley","year":"1999","unstructured":"Kelley, C.T.: Iterative Methods for Optimization, pp. 102\u2013104. SIAM, Philadelphia (1999)"},{"key":"228_CR15","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.orl.2011.01.004","volume":"39","author":"QN Li","year":"2011","unstructured":"Li, Q.N., Li, D.H.: A projected semi-smooth Newton method for problems of calibrating least squares covariance matrix. Oper. Res. Lett. 39, 103\u2013108 (2011)","journal-title":"Oper. Res. Lett."},{"key":"228_CR16","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/BF01589116","volume":"45","author":"DC Liu","year":"1989","unstructured":"Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large-scale optimization. Math. Program. 45, 503\u2013528 (1989)","journal-title":"Math. Program."},{"key":"228_CR17","doi-asserted-by":"publisher","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."},{"issue":"4","key":"228_CR18","doi-asserted-by":"publisher","first-page":"569","DOI":"10.3938\/jkps.62.569","volume":"62","author":"A Nobi","year":"2013","unstructured":"Nobi, A., Maeng, S.E., Ha, G.G., Lee, J.W.: Random matrix theory and cross-correlations in global financial indices and local stock market indices. J. Korean Phys. Soc. 62(4), 569\u2013574 (2013)","journal-title":"J. Korean Phys. Soc."},{"key":"228_CR19","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.physa.2014.03.083","volume":"407","author":"A Nobi","year":"2014","unstructured":"Nobi, A., Maeng, S.E., Ha, G.G., Lee, J.W.: Effects of global financial crisis on network structure in a local stock market. Phys. A 407, 135\u2013143 (2014)","journal-title":"Phys. A"},{"key":"228_CR20","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Berlin (2006)","edition":"2"},{"key":"228_CR21","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1287\/moor.18.1.227","volume":"18","author":"LQ Qi","year":"1993","unstructured":"Qi, L.Q.: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18, 227\u2013244 (1993)","journal-title":"Math. Oper. Res."},{"issue":"1\u20133","key":"228_CR22","first-page":"277","volume":"64","author":"LQ Qi","year":"1994","unstructured":"Qi, L.Q.: Superlinearly convergent approximate Newton methods for LC$$^1$$ optimization problems. Math. Program. 64(1\u20133), 277\u2013294 (1994)","journal-title":"Math. Program."},{"key":"228_CR23","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/BF01581275","volume":"58","author":"LQ Qi","year":"1993","unstructured":"Qi, L.Q., Sun, J.: A nonsmooth version of Newton\u2019s method. Math. Program. 58, 353\u2013367 (1993)","journal-title":"Math. Program."},{"key":"228_CR24","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1137\/050624509","volume":"28","author":"HD 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."},{"key":"228_CR25","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970524","volume-title":"Conjugate Duality and Optimization","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Conjugate Duality and Optimization. SIAM, Philadelphia (1974)"},{"key":"228_CR26","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1080\/00949657908810316","volume":"9","author":"NC Schwertman","year":"1979","unstructured":"Schwertman, N.C., Allen, D.M.: Smoothing an indefinite variance\u2013covariance matrix. J. Stat. Comput. Simul. 9, 183\u2013194 (1979)","journal-title":"J. Stat. Comput. Simul."},{"key":"228_CR27","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s40314-020-1089-9","volume":"39","author":"CG Shen","year":"2020","unstructured":"Shen, C.G., Fan, C.X., Wang, Y.L., Xue, W.J.: Limited memory BFGS algorithm for the matrix approximation problem in Frobenius norm. Comput. Appl. Math. 39, 43 (2020)","journal-title":"Comput. Appl. Math."},{"key":"228_CR28","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.najef.2013.02.007","volume":"26","author":"MKP So","year":"2013","unstructured":"So, M.K.P., Wang, J., Asai, M.: Stress testing correlation matrices for risk management. North Am. J. Econ. Finance 26, 310\u2013322 (2013)","journal-title":"North Am. J. Econ. Finance"},{"issue":"1","key":"228_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0370-1573(02)00634-8","volume":"378","author":"D Sornette","year":"2003","unstructured":"Sornette, D.: Critical market crashes. Phys. Rep. 378(1), 1\u201398 (2003)","journal-title":"Phys. Rep."},{"key":"228_CR30","doi-asserted-by":"publisher","DOI":"10.23943\/princeton\/9780691175959.001.0001","volume-title":"Why Stock Markets Crash: Critical Events in Complex Financial Systems","author":"D Sornette","year":"2017","unstructured":"Sornette, D.: Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press, Princeton (2017)"},{"key":"228_CR31","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"JF Sturm","year":"1999","unstructured":"Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11, 625\u2013653 (1999)","journal-title":"Optim. Methods Softw."},{"key":"228_CR32","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1287\/moor.27.1.150.342","volume":"27","author":"DF Sun","year":"2002","unstructured":"Sun, D.F., Sun, J.: Semi-smooth matrix valued functions. Math. Oper. Res. 27, 150\u2013169 (2002)","journal-title":"Math. Oper. Res."},{"key":"228_CR33","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1137\/15M1011020","volume":"36","author":"YF Sun","year":"2015","unstructured":"Sun, Y.F., Vandenberghe, L.: Decomposition methods for sparse matrix nearness problems. SIAM J. Matrix Anal. Appl. 36, 1691\u20131717 (2015)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"228_CR34","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10107-002-0347-5","volume":"95","author":"RH T\u00fct\u00fcnc\u00fc","year":"2003","unstructured":"T\u00fct\u00fcnc\u00fc, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. 95, 189\u2013217 (2003)","journal-title":"Math. Program."},{"key":"228_CR35","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1080\/10556780600552693","volume":"22","author":"CH Ye","year":"2007","unstructured":"Ye, C.H., Yuan, X.M.: A descent method for structured monotone variational inequalities. Optim. Methods Softw. 22, 329\u2013338 (2007)","journal-title":"Optim. Methods Softw."},{"key":"228_CR36","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"H Zhang","year":"2004","unstructured":"Zhang, H., Hager, W.W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14, 1043\u20131056 (2004)","journal-title":"SIAM J. Optim."},{"key":"228_CR37","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10589-006-6446-0","volume":"35","author":"B Zhou","year":"2006","unstructured":"Zhou, B., Gao, L., Dai, Y.H.: Gradient methods with adaptive step-sizes. Comput. Optim. Appl. 35, 69\u201386 (2006)","journal-title":"Comput. Optim. Appl."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-020-00228-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-020-00228-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-020-00228-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,26]],"date-time":"2021-09-26T23:44:16Z","timestamp":1632699856000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-020-00228-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,27]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["228"],"URL":"https:\/\/doi.org\/10.1007\/s10589-020-00228-5","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,27]]},"assertion":[{"value":"9 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}