{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:44:55Z","timestamp":1757313895707,"version":"3.37.3"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T00:00:00Z","timestamp":1666742400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T00:00:00Z","timestamp":1666742400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871153, 12271097"],"award-info":[{"award-number":["11871153, 12271097"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2019J01644"],"award-info":[{"award-number":["2019J01644"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s10957-022-02120-0","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T14:02:44Z","timestamp":1666792964000},"page":"749-779","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Semismooth Newton-based Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems"],"prefix":"10.1007","volume":"195","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6586-2862","authenticated-orcid":false,"given":"Yong-Jin","family":"Liu","sequence":"first","affiliation":[]},{"given":"Jing","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,26]]},"reference":[{"key":"2120_CR1","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s10107-018-1351-8","volume":"174","author":"AY Aravkin","year":"2019","unstructured":"Aravkin, A.Y., Burke, J., Drusvyatskiy, D., Friedlander, M.P., Roy, S.: Level-set methods for convex optimization. Math. Program. 174, 359\u2013390 (2019)","journal-title":"Math. Program."},{"key":"2120_CR2","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1137\/S0036144593251710","volume":"38","author":"HH Bauschke","year":"1996","unstructured":"Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Rev. 38, 367\u2013426 (1996)","journal-title":"SIAM Rev."},{"key":"2120_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974997","volume-title":"First-Order Methods in Optimization","author":"A Beck","year":"2017","unstructured":"Beck, A.: First-Order Methods in Optimization. SIAM, Philadephia (2017)"},{"key":"2120_CR4","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"2120_CR5","volume-title":"Matrix Analysis","author":"R Bhatia","year":"2013","unstructured":"Bhatia, R.: Matrix Analysis. Springer-Verlag, New York (2013)"},{"key":"2120_CR6","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1287\/moor.2019.1008","volume":"45","author":"RI Bot","year":"2020","unstructured":"Bot, R.I., Nguyen, D.K.: The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates. Math. Oper. Res. 45, 682\u2013712 (2020)","journal-title":"Math. Oper. Res."},{"key":"2120_CR7","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"EJ Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9, 717\u2013772 (2009)","journal-title":"Found. Comput. Math."},{"key":"2120_CR8","doi-asserted-by":"publisher","first-page":"1241","DOI":"10.1002\/cpa.21432","volume":"66","author":"EJ Cand\u00e8s","year":"2013","unstructured":"Cand\u00e8s, E.J., Strohmer, T., Voroninski, V.: PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming. Commun. Pure Appl. Math. 66, 1241\u20131274 (2013)","journal-title":"Commun. Pure Appl. Math."},{"key":"2120_CR9","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1093\/imanum\/drq039","volume":"32","author":"CH Chen","year":"2012","unstructured":"Chen, C.H., He, B.S., Yuan, X.M.: Matrix completion via alternating direction methods. IMA J. Numer. Anal. 32, 227\u2013245 (2012)","journal-title":"IMA J. Numer. Anal."},{"key":"2120_CR10","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971309","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1990","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. SIAM, Philadephia (1990)"},{"key":"2120_CR11","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s40305-021-00346-9","volume":"10","author":"Y Cui","year":"2022","unstructured":"Cui, Y., Ding, C., Li, X.D., Zhao, X.Y.: Augmented Lagrangian methods for convex matrix optimization problems. J. Oper. Res. Soc. China 10, 305\u2013342 (2022)","journal-title":"J. Oper. Res. Soc. China"},{"key":"2120_CR12","unstructured":"Cui, Y., Sun, D.F., Toh, K.-C.: On the asymptotic superlinear convergence of the augmented Lagrangian method for semidefinite programming with multiple solutions. arXiv preprint arXiv: 1610.00875, (2016)"},{"key":"2120_CR13","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s10107-018-1300-6","volume":"178","author":"Y Cui","year":"2019","unstructured":"Cui, Y., Sun, D.F., Toh, K.-C.: On the R-superlinear convergence of the KKT residuals generated by the augmented Lagrangian method for convex composite conic programming. Math. Program. 178, 381\u2013415 (2019)","journal-title":"Math. Program."},{"key":"2120_CR14","unstructured":"Ding, C.: An introduction to a class of matrix optimization problems. Ph.D. thesis, National University of Singapore (2012)"},{"key":"2120_CR15","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/s10107-017-1162-3","volume":"168","author":"C Ding","year":"2018","unstructured":"Ding, C., Sun, D.F., Toh, K.-C.: Spectral operators of matrices. Math. Program. 168, 509\u2013531 (2018)","journal-title":"Math. Program."},{"key":"2120_CR16","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1137\/18M1222235","volume":"30","author":"C Ding","year":"2020","unstructured":"Ding, C., Sun, D.F., Sun, J., Toh, K.-C.: Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian. SIAM J. Optim. 30, 630\u2013659 (2020)","journal-title":"SIAM J. Optim."},{"key":"2120_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87821-8","volume-title":"Implicit Functions and Solution Mappings","author":"AL Dontchev","year":"2009","unstructured":"Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. Springer, New York (2009)"},{"key":"2120_CR18","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293\u2013318 (1992)","journal-title":"Math. Program."},{"key":"2120_CR19","volume-title":"Finite-dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.-S.: Finite-dimensional Variational Inequalities and Complementarity Problems. Springer-Verlag, New York (2003)"},{"key":"2120_CR20","unstructured":"Fazel, M.: Matrix rank minimization with applications. Ph.D. thesis, Stanford University (2002)"},{"key":"2120_CR21","doi-asserted-by":"crossref","unstructured":"Fazel, M., Hindi, H., Boyd, S.: A rank minimization heuristic with application to minimum order system approximation. In: Proceedings of the American Control Conference (2001)","DOI":"10.1109\/ACC.2001.945730"},{"key":"2120_CR22","doi-asserted-by":"publisher","first-page":"A1616","DOI":"10.1137\/15M1034283","volume":"38","author":"MP Friedlander","year":"2016","unstructured":"Friedlander, M.P., Mac\u00eado, I.: Low-rank spectral optimization via gauge duality. SIAM J. Sci. Comput. 38, A1616\u2013A1638 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"2120_CR23","doi-asserted-by":"publisher","first-page":"1999","DOI":"10.1137\/130940785","volume":"24","author":"MP Friedlander","year":"2014","unstructured":"Friedlander, M.P., Mac\u00eado, I., Pong, T.K.: Gauge optimization and duality. SIAM J. Optim. 24, 1999\u20132022 (2014)","journal-title":"SIAM J. Optim."},{"key":"2120_CR24","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 approximation. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"2120_CR25","first-page":"41","volume":"2","author":"R Glowinski","year":"1975","unstructured":"Glowinski, R., Marroco, A.: Sur l\u2019approximation, par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9 d\u2019une classe de probl\u00e9mes de Dirichlet non lin\u00e9aires. J. Equine Vet. Sci. 2, 41\u201376 (1975)","journal-title":"J. Equine Vet. Sci."},{"key":"2120_CR26","unstructured":"Guo, H.: The metric subregularity of KKT solution mappings of composite conic programming. Ph.D. thesis, National University of Singapore (2017)"},{"key":"2120_CR27","doi-asserted-by":"crossref","unstructured":"Hazan, E.: Sparse approximate solutions to semidefinite programs. In: Latin American Symposium on Theoretical Informatics 4957, 306\u2013316 (2008)","DOI":"10.1007\/978-3-540-78773-0_27"},{"key":"2120_CR28","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/BF01580223","volume":"6","author":"M Held","year":"1974","unstructured":"Held, M., Wolfe, P., Crowder, H.P.: Validation of subgradient optimization. Math. Program. 6, 62\u201388 (1974)","journal-title":"Math. Program."},{"key":"2120_CR29","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/BF01442169","volume":"11","author":"JB Hiriart-Urruty","year":"1984","unstructured":"Hiriart-Urruty, J.B., Strodiot, J.J., Nguyen, V.H.: Generalized Hessian matrix and second-order optimality conditions for problems with $$C^{1,1}$$ data. Appl. Math. Optim. 11, 43\u201356 (1984)","journal-title":"Appl. Math. Optim."},{"key":"2120_CR30","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/978-3-319-00200-2_9","volume":"69","author":"KF Jiang","year":"2013","unstructured":"Jiang, K.F., Sun, D.F., Toh, K.-C.: Solving nuclear norm regularized and semidefinite matrix least squares problems with linear equality constraints. Discrete Geom. Optim. 69, 133\u2013162 (2013)","journal-title":"Discrete Geom. Optim."},{"key":"2120_CR31","unstructured":"Korpas, G., Marecek, J.: Quantum state tomography as a bilevel problem, utilizing I-Q plane data. arxiv preprint arxiv:2108.03448, (2021)"},{"key":"2120_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41534-018-0080-4","volume":"4","author":"A Kyrillidis","year":"2018","unstructured":"Kyrillidis, A., Kalev, A., Park, D., Bhojanapalli, S.: Provable compressed sensing quantum state tomography via non-convex methods. npj Quantum Inform. 4, 1\u20137 (2018)","journal-title":"npj Quantum Inform."},{"key":"2120_CR33","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1137\/S1052623494267127","volume":"7","author":"C Lemar\u00e9chal","year":"1997","unstructured":"Lemar\u00e9chal, C., Sagastiz\u00e1bal, C.: Practical aspects of the Moreau-Yosida regularization: theoretical preliminaries. SIAM J. Optim. 7, 367\u2013385 (1997)","journal-title":"SIAM J. Optim."},{"key":"2120_CR34","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1287\/moor.21.3.576","volume":"21","author":"AS Lewis","year":"1996","unstructured":"Lewis, A.S.: Derivatives of spectral functions. Math. Oper. Res. 21, 576\u2013588 (1996)","journal-title":"Math. Oper. Res."},{"key":"2120_CR35","unstructured":"Li, X.D.: A two-phase augmented Lagrangian method for convex composite quadratic programming. Ph.D. thesis, National University of Singapore (2015)"},{"key":"2120_CR36","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1137\/16M1097572","volume":"28","author":"XD Li","year":"2018","unstructured":"Li, X.D., Sun, D.F., Toh, K.-C.: A highly efficient semismooth Newton augmented Lagrangian method for solving lasso problems. SIAM J. Optim. 28, 433\u2013458 (2018)","journal-title":"SIAM J. Optim."},{"key":"2120_CR37","doi-asserted-by":"publisher","first-page":"1842","DOI":"10.1137\/17M1136390","volume":"28","author":"XD Li","year":"2018","unstructured":"Li, X.D., Sun, D.F., Toh, K.-C.: On efficiently solving the subproblems of a level-set method for fused lasso problems. SIAM J. Optim. 28, 1842\u20131866 (2018)","journal-title":"SIAM J. Optim."},{"key":"2120_CR38","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/s12532-018-0137-6","volume":"10","author":"XD Li","year":"2018","unstructured":"Li, X.D., Sun, D.F., Toh, K.-C.: QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming. Math. Program. Comput. 10, 703\u2013743 (2018)","journal-title":"Math. Program. Comput."},{"key":"2120_CR39","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s10107-018-1342-9","volume":"179","author":"XD Li","year":"2020","unstructured":"Li, X.D., Sun, D.F., Toh, K.-C.: On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope. Math. Program. 179, 419\u2013446 (2020)","journal-title":"Math. Program."},{"key":"2120_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-021-01541-9","volume":"88","author":"LY Lin","year":"2021","unstructured":"Lin, L.Y., Liu, Y.-J.: An efficient Hessian based algorithm for singly linearly and box constrained least squares regression. J. Sci. Comput. 88, 1\u201321 (2021)","journal-title":"J. Sci. Comput."},{"key":"2120_CR41","doi-asserted-by":"publisher","first-page":"2026","DOI":"10.1137\/18M1207752","volume":"29","author":"MX Lin","year":"2019","unstructured":"Lin, M.X., Liu, Y.-J., Sun, D.F., Toh, K.-C.: Efficient sparse semismooth Newton methods for the clustered lasso problem. SIAM J. Optim. 29, 2026\u20132052 (2019)","journal-title":"SIAM J. Optim."},{"key":"2120_CR42","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01170633","volume":"38","author":"K L\u00f6wner","year":"1934","unstructured":"L\u00f6wner, K.: \u00dcber monotone matrixfunktionen. Math. Z. 38, 177\u2013216 (1934)","journal-title":"Math. Z."},{"key":"2120_CR43","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0167-6377(88)90047-8","volume":"7","author":"OL Mangasarian","year":"1988","unstructured":"Mangasarian, O.L.: A simple characterization of solution sets of convex programs. Oper. Res. Lett. 7, 21\u201326 (1988)","journal-title":"Oper. Res. Lett."},{"key":"2120_CR44","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1007\/s10107-005-0629-9","volume":"104","author":"FW Meng","year":"2005","unstructured":"Meng, F.W., Sun, D.F., Zhao, G.Y.: Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization. Math. Program. 104, 561\u2013581 (2005)","journal-title":"Math. Program."},{"key":"2120_CR45","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1137\/0315061","volume":"15","author":"R Mifflin","year":"1977","unstructured":"Mifflin, R.: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control Optim. 15, 957\u2013972 (1977)","journal-title":"SIAM J. Control Optim."},{"key":"2120_CR46","doi-asserted-by":"publisher","first-page":"273","DOI":"10.24033\/bsmf.1625","volume":"93","author":"JJ Moreau","year":"1965","unstructured":"Moreau, J.J.: Proximit\u00e9 et dualit\u00e9 dans un espace hilbertien. B. Soc. Math. Fr. 93, 273\u2013299 (1965)","journal-title":"B. Soc. Math. Fr."},{"key":"2120_CR47","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2002","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. The University Press, Cambridge (2002)"},{"key":"2120_CR48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/PL00011388","volume":"89","author":"F Oustry","year":"2000","unstructured":"Oustry, F.: A second-order bundle method to minimize the maximum eigenvalue function. Math. Program. 89, 1\u201333 (2000)","journal-title":"Math. Program."},{"key":"2120_CR49","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1137\/14095697X","volume":"8","author":"Y Ouyang","year":"2014","unstructured":"Ouyang, Y., Chen, Y., Lan, G., Pasiliao, J.E.: An accelerated linearized alternating direction method of multipliers. SIAM J. Imaging Sci. 8, 644\u2013681 (2014)","journal-title":"SIAM J. Imaging Sci."},{"key":"2120_CR50","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1137\/0802007","volume":"2","author":"ML Overton","year":"1992","unstructured":"Overton, M.L.: Large-scale optimization of eigenvalues. SIAM J. Optim. 2, 88\u2013120 (1992)","journal-title":"SIAM J. Optim."},{"key":"2120_CR51","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1137\/070697835","volume":"3","author":"B Recht","year":"2010","unstructured":"Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 3, 471\u2013501 (2010)","journal-title":"SIAM Rev."},{"key":"2120_CR52","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1007\/BFb0120929","volume":"14","author":"SM Robinson","year":"1981","unstructured":"Robinson, S.M.: Some continuity properties of polyhedral multifunctions. Math. Program. Stud. 14, 206\u2013214 (1981)","journal-title":"Math. Program. Stud."},{"key":"2120_CR53","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"2120_CR54","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":"2120_CR55","first-page":"615","volume":"6","author":"K-C Toh","year":"2010","unstructured":"Toh, K.-C., Yun, S.W.: An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems. Pac. J. Optim. 6, 615\u2013640 (2010)","journal-title":"Pac. J. Optim."},{"key":"2120_CR56","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10107-013-0738-9","volume":"149","author":"I Waldspurger","year":"2015","unstructured":"Waldspurger, I., d\u2019Aspremont, A., Mallat, S.: Phase recovery, MaxCut and complex semidefinite programming. Math. Program. 149, 47\u201381 (2015)","journal-title":"Math. Program."},{"key":"2120_CR57","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s12532-015-0082-6","volume":"7","author":"LQ Yang","year":"2015","unstructured":"Yang, L.Q., Sun, D.F., Toh, K.-C.: SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints. Math. Program. Comput. 7, 331\u2013366 (2015)","journal-title":"Math. Program. Comput."},{"key":"2120_CR58","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1137\/090777761","volume":"33","author":"JF Yang","year":"2011","unstructured":"Yang, J.F., Zhang, Y.: Alternating direction algorithms for $$l_1$$-problems in compressive sensing. SIAM J. Sci. Comput. 33, 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"2120_CR59","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s10107-018-1329-6","volume":"179","author":"YJ Zhang","year":"2020","unstructured":"Zhang, Y.J., Zhang, N., Sun, D.F., Toh, K.-C.: An efficient Hessian based algorithm for solving large-scale sparse group lasso problems. Math. Program. 179, 223\u2013263 (2020)","journal-title":"Math. Program."},{"key":"2120_CR60","doi-asserted-by":"publisher","first-page":"1737","DOI":"10.1137\/080718206","volume":"20","author":"XY Zhao","year":"2010","unstructured":"Zhao, X.Y., Sun, D.F., Toh, K.-C.: A Newton-CG augmented Lagrangian method for semidefinite programming. SIAM J. Optim. 20, 1737\u20131765 (2010)","journal-title":"SIAM J. Optim."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02120-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02120-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02120-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T03:37:25Z","timestamp":1668656245000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02120-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,26]]},"references-count":60,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["2120"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02120-0","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2022,10,26]]},"assertion":[{"value":"9 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}