{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T12:40:57Z","timestamp":1777552857457,"version":"3.51.4"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,5,2]],"date-time":"2009-05-02T00:00:00Z","timestamp":1241222400000},"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":[[2011,3]]},"DOI":"10.1007\/s10589-009-9253-6","type":"journal-article","created":{"date-parts":[[2009,5,4]],"date-time":"2009-05-04T16:07:43Z","timestamp":1241453263000},"page":"233-253","source":"Crossref","is-referenced-by-count":19,"title":["Convex constrained optimization for large-scale generalized Sylvester equations"],"prefix":"10.1007","volume":"48","author":[{"given":"A.","family":"Bouhamidi","sequence":"first","affiliation":[]},{"given":"K.","family":"Jbilou","sequence":"additional","affiliation":[]},{"given":"M.","family":"Raydan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,5,2]]},"reference":[{"key":"9253_CR1","volume-title":"Optimal Control of Distributed Parameter Systems","author":"N.V. Ahmed","year":"1981","unstructured":"Ahmed, N.V., Teo, K.L.: Optimal Control of Distributed Parameter Systems. North-Holland, Amsterdam (1981)"},{"key":"9253_CR2","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1109\/TSMC.1976.4309481","volume":"6","author":"G.L. Anderson","year":"1976","unstructured":"Anderson, G.L., Netravali, A.N.: Image restoration based on a subjective criterion. IEEE Trans. Syst. Man Cybern. 6, 845\u2013856 (1976)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"9253_CR3","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1145\/361573.361582","volume":"15","author":"R.H. Bartels","year":"1972","unstructured":"Bartels, R.H., Stewart, G.W.: Solution of the matrix equation AX+XB=C. Commun. ACM 15, 820\u2013826 (1972)","journal-title":"Commun. ACM"},{"key":"9253_CR4","doi-asserted-by":"crossref","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":"9253_CR5","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/TAC.1976.1101194","volume":"21","author":"D.P. Bertsekas","year":"1976","unstructured":"Bertsekas, D.P.: On The Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Automat. Contr. 21, 174\u2013184 (1976)","journal-title":"IEEE Trans. Automat. Contr."},{"key":"9253_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. Opt. 10, 1196\u20131211 (2000)","journal-title":"SIAM J. Opt."},{"key":"9253_CR7","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\u2014software for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340\u2013349 (2001)","journal-title":"ACM Trans. Math. Softw."},{"key":"9253_CR8","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/imanum\/23.4.539","volume":"23","author":"E.G. Birgin","year":"2003","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Inexact spectral gradient method for convex-constrained optimization. IMA J. Numer. Anal. 23, 539\u2013559 (2003)","journal-title":"IMA J. Numer. Anal."},{"key":"9253_CR9","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.cam.2006.05.028","volume":"206","author":"A. Bouhamidi","year":"2007","unstructured":"Bouhamidi, A., Jbilou, K.: Sylvester Tikhonov-regularization methods in image restoration. J. Comput. Math. 206, 86\u201398 (2007)","journal-title":"J. Comput. Math."},{"key":"9253_CR10","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/978-1-4613-9940-7_3","volume":"37","author":"J.P. Boyle","year":"1986","unstructured":"Boyle, J.P., Dykstra, R.L.: A method for finding projections onto the intersection of convex sets in Hilbert spaces. Lect. Notes Stat. 37, 28\u201347 (1986)","journal-title":"Lect. Notes Stat."},{"key":"9253_CR11","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0377-0427(97)00149-0","volume":"86","author":"D. Calvetti","year":"1997","unstructured":"Calvetti, D., Levenberg, N., Reichel, L.: Iterative methods for X\u2212AXB=C. J. Comput. Appl. Math. 86, 73\u2013101 (1997)","journal-title":"J. Comput. Appl. Math."},{"key":"9253_CR12","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1023\/A:1022383005969","volume":"39","author":"D. Calvetti","year":"1999","unstructured":"Calvetti, D., Golub, G.H., Reichel, L.: Estimation of the L-curve via Lanczos bidiagonalization. BIT 39, 603\u2013619 (1999)","journal-title":"BIT"},{"key":"9253_CR13","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1023\/A:1021918118380","volume":"42","author":"D. Calvetti","year":"2002","unstructured":"Calvetti, D., Lewis, B., Reichel, L.: GMRES, L-curves and discrete ill-posed problems. BIT 42, 44\u201365 (2002)","journal-title":"BIT"},{"key":"9253_CR14","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S0168-9274(01)00179-9","volume":"43","author":"J.L. Castellanos","year":"2002","unstructured":"Castellanos, J.L., G\u00f3mez, S., Guerra, V.: The triangle method for finding the corner of the L-curve. Appl. Numer. Math. 43, 359\u2013373 (2002)","journal-title":"Appl. Numer. Math."},{"key":"9253_CR15","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717877","volume-title":"Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods","author":"T.F. Chan","year":"2005","unstructured":"Chan, T.F., Shen, J.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)"},{"key":"9253_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/22.1.1","volume":"22","author":"Y.H. Dai","year":"2002","unstructured":"Dai, Y.H., Liao, L.Z.: R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 22, 1\u201310 (2002)","journal-title":"IMA J. Numer. Anal."},{"key":"9253_CR17","volume-title":"Numerical Methods for Linear Control Systems Design and Analysis","author":"B.N. Datta","year":"2003","unstructured":"Datta, B.N.: Numerical Methods for Linear Control Systems Design and Analysis. Elsevier, Amsterdam (2003)"},{"key":"9253_CR18","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1137\/0609010","volume":"9","author":"J.W. Demmel","year":"1988","unstructured":"Demmel, J.W., K\u00e5gstr\u00f6m, B.: Accurate solutions of ill-posed problems in control theory. SIAM J. Matrix Anal. Appl. 9, 126\u2013145 (1988)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9253_CR19","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1137\/0114057","volume":"14","author":"A. Dou","year":"1966","unstructured":"Dou, A.: Method of undetermined coefficients in linear differential systems and the matrix equation YA\u2212AY=F. SIAM J. Appl. Math. 14, 691\u2013696 (1966)","journal-title":"SIAM J. Appl. Math."},{"key":"9253_CR20","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1023\/A:1014807923223","volume":"29","author":"A. El Guennouni","year":"2002","unstructured":"El Guennouni, A., Jbilou, K., Riquet, A.J.: Block Krylov subspace methods for solving large Sylvester equations. Numer. Algorithms 29, 75\u201396 (2002)","journal-title":"Numer. Algorithms"},{"key":"9253_CR21","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01932775","volume":"20","author":"M.A. Epton","year":"1980","unstructured":"Epton, M.A.: Methods for the solution of AXD\u2212BXC=E and its application in the numerical solution of implicit ordinary differential equations. BIT 20, 341\u2013345 (1980)","journal-title":"BIT"},{"key":"9253_CR22","first-page":"165","volume":"26","author":"R. Fletcher","year":"1990","unstructured":"Fletcher, R.: Low storage methods for unconstrained optimization. Lect. Appl. Math. 26, 165\u2013179 (1990)","journal-title":"Lect. Appl. Math."},{"key":"9253_CR23","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/0-387-24255-4_10","volume-title":"Optimization and Control with Applications","author":"R. Fletcher","year":"2005","unstructured":"Fletcher, R.: On the Barzilai-Borwein method. In: Qi, L., Teo, K.L., Yang, X.Q. (eds.) Optimization and Control with Applications, pp. 235\u2013256. Springer, Berlin (2005)"},{"key":"9253_CR24","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1090\/S0002-9904-1964-11178-2","volume":"70","author":"A.A. Goldstein","year":"1964","unstructured":"Goldstein, A.A.: Convex Programming in Hilbert Space. Bull. Am. Math. Soc. 70, 709\u2013710 (1964)","journal-title":"Bull. Am. Math. Soc."},{"key":"9253_CR25","first-page":"3","volume-title":"Workshop on Scientific Computing","author":"G.H. Golub","year":"1997","unstructured":"Golub, G.H., von Matt, U.: Tikhonov regularization for large scale problems. In: Golub, G.H., Lui, S.H., Luk, F., Plemmons, R. (eds.) Workshop on Scientific Computing, pp. 3\u201326. Springer, New York (1997)"},{"key":"9253_CR26","doi-asserted-by":"crossref","first-page":"215","DOI":"10.2307\/1268518","volume":"21","author":"G.H. Golub","year":"1979","unstructured":"Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215\u2013223 (1979)","journal-title":"Technometrics"},{"key":"9253_CR27","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1109\/TAC.1979.1102170","volume":"24","author":"G.H. Golub","year":"1979","unstructured":"Golub, G.H., Nash, S., Van Loan, C.: A Hessenberg-Schur method the problem AX+XB=C. IEEE Trans. Automat. Contr. AC 24, 909\u2013913 (1979)","journal-title":"IEEE Trans. Automat. Contr. AC"},{"key":"9253_CR28","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L. Grippo","year":"1986","unstructured":"Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton\u2019s method. SIAM J. Numer. Anal. 23, 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"9253_CR29","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1093\/imanum\/2.3.303","volume":"2","author":"S.J. Hammarling","year":"1982","unstructured":"Hammarling, S.J.: Numerical solution of the stable, nonnegative definite Lyapunov equations. IMA J. Numer. Anal. 2, 303\u2013323 (1982)","journal-title":"IMA J. Numer. Anal."},{"key":"9253_CR30","first-page":"253","volume":"3","author":"M. Hanke","year":"1993","unstructured":"Hanke, M., Hansen, P.C.: Regularization methods for large-scale problems. Surv. Math. Ind. 3, 253\u2013315 (1993)","journal-title":"Surv. Math. Ind."},{"key":"9253_CR31","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1137\/1034115","volume":"34","author":"P.C. Hansen","year":"1992","unstructured":"Hansen, P.C.: Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev. 34, 561\u2013580 (1992)","journal-title":"SIAM Rev."},{"key":"9253_CR32","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718874","volume-title":"Deblurring Images: Matrices, Spectra, and Filtering","author":"P.C. Hansen","year":"2006","unstructured":"Hansen, P.C., Nagy, J.G., O\u2019Leary, D.P.: Deblurring Images: Matrices, Spectra, and Filtering. SIAM, Philadelphia (2006)"},{"key":"9253_CR33","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/0024-3795(92)90031-5","volume":"174","author":"D.Y. Hu","year":"1992","unstructured":"Hu, D.Y., Reichel, L.: Krylov subspace methods for the Sylvester equation. Linear Algebra Appl. 174, 283\u2013314 (1992)","journal-title":"Linear Algebra Appl."},{"key":"9253_CR34","first-page":"227","volume":"31","author":"I.M. Jaimoukha","year":"1994","unstructured":"Jaimoukha, I.M., Kasenally, E.M.: Krylov subspace methods for solving large Lyapunov equations. SIAM J. Matrix Anal. Appl. 31, 227\u2013251 (1994)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9253_CR35","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.amc.2005.11.014","volume":"177","author":"K. Jbilou","year":"2006","unstructured":"Jbilou, K.: Low rank approximate solutions to large Sylvester matrix equations. Appl. Math. Comput. 177, 365\u2013376 (2006)","journal-title":"Appl. Math. Comput."},{"key":"9253_CR36","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.laa.2004.11.004","volume":"415","author":"K. Jbilou","year":"2006","unstructured":"Jbilou, K., Riquet, A.: Projection methods for large Lyapunov matrix equations. Linear Algebra Appl. 415, 344\u2013358 (2006)","journal-title":"Linear Algebra Appl."},{"key":"9253_CR37","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0168-9274(98)00094-4","volume":"31","author":"K. Jbilou","year":"1999","unstructured":"Jbilou, K., Messaoudi, A., Sadok, H.: Global FOM and GMRES algorithms for matrix equations. Appl. Numer. Math. 31, 49\u201363 (1999)","journal-title":"Appl. Numer. Math."},{"key":"9253_CR38","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1090\/S0025-5718-06-01836-9","volume":"75","author":"W. La Cruz","year":"2006","unstructured":"La Cruz, W., Mart\u00ednez, J.M., Raydan, M.: Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75, 1449\u20131466 (2006)","journal-title":"Math. Comput."},{"key":"9253_CR39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0041-5553(66)90114-5","volume":"6","author":"E.S. Levitin","year":"1966","unstructured":"Levitin, E.S., Polyak, B.T.: Constrained minimization problems. U.S.S.R. Comput. Math. Math. Phys. 6, 1\u201350 (1966)","journal-title":"U.S.S.R. Comput. Math. Math. Phys."},{"key":"9253_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65024-6","volume-title":"Optimal Control of Systems Governed by Partial Differential Equations","author":"J.L. Lions","year":"1971","unstructured":"Lions, J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, Berlin (1971)"},{"key":"9253_CR41","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1086\/111605","volume":"79","author":"L.B. Lucy","year":"1974","unstructured":"Lucy, L.B.: An iterative technique for the rectification of observed distributions. Astron. J. 79, 745\u2013754 (1974)","journal-title":"Astron. J."},{"key":"9253_CR42","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1590\/S1807-03022008000100003","volume":"27","author":"M. Monsalve","year":"2008","unstructured":"Monsalve, M.: Block linear method for large scale Sylvester equations. Comput. Appl. Math. 27, 47\u201359 (2008)","journal-title":"Comput. Appl. Math."},{"key":"9253_CR43","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1093\/imanum\/13.3.321","volume":"13","author":"M. Raydan","year":"1993","unstructured":"Raydan, M.: On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13, 321\u2013326 (1993)","journal-title":"IMA J. Numer. Anal."},{"key":"9253_CR44","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1364\/JOSA.62.000055","volume":"62","author":"W.H. Richardson","year":"1972","unstructured":"Richardson, W.H.: Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62, 55\u201359 (1972)","journal-title":"J. Opt. Soc. Am."},{"key":"9253_CR45","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1007\/BF01733793","volume":"36","author":"V. Simoncini","year":"1996","unstructured":"Simoncini, V.: On the numerical solution of AX\u2212XB=C. BIT 36, 814\u2013830 (1996)","journal-title":"BIT"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9253-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-009-9253-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9253-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:36Z","timestamp":1559288196000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-009-9253-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,2]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["9253"],"URL":"https:\/\/doi.org\/10.1007\/s10589-009-9253-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,2]]}}}