{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T21:41:49Z","timestamp":1778708509516,"version":"3.51.4"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T00:00:00Z","timestamp":1310515200000},"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":[[2012,6]]},"DOI":"10.1007\/s10589-011-9420-4","type":"journal-article","created":{"date-parts":[[2011,7,12]],"date-time":"2011-07-12T11:40:05Z","timestamp":1310470805000},"page":"345-371","source":"Crossref","is-referenced-by-count":22,"title":["Scaling linear optimization problems prior to application of the simplex method"],"prefix":"10.1007","volume":"52","author":[{"given":"Joseph M.","family":"Elble","sequence":"first","affiliation":[]},{"given":"Nikolaos V.","family":"Sahinidis","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,7,13]]},"reference":[{"key":"9420_CR1","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF01385880","volume":"5","author":"F.L. Bauer","year":"1963","unstructured":"Bauer, F.L.: Optimally scaled matrices. Numer. Math. 5, 73\u201387 (1963)","journal-title":"Numer. Math."},{"key":"9420_CR2","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1007\/BF01584344","volume":"13","author":"M. Benichou","year":"1977","unstructured":"Benichou, M., Gauthier, J.M., Hentges, G., Ribiere, G.: The efficient solution of large-scale linear programming problems\u2014Some algorithmic techniques and computational results. Math. Program. 13, 280\u2013322 (1977)","journal-title":"Math. Program."},{"key":"9420_CR3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1287\/opre.50.1.3.17780","volume":"50","author":"R.E. Bixby","year":"2002","unstructured":"Bixby, R.E.: Solving real-world linear programs: A decade and more of progress. Oper. Res. 50, 3\u201315 (2002)","journal-title":"Oper. Res."},{"key":"9420_CR4","unstructured":"Bradley, A.: Algorithms for the equilibration of matrices and their application to limited-memory quasi-Newton methods. PhD thesis, Stanford University, Stanford, California (2010)"},{"key":"9420_CR5","volume-title":"Linear Programming","author":"V. Chv\u00e1tal","year":"1983","unstructured":"Chv\u00e1tal, V.: Linear Programming. W.H. Freeman, New York (1983)"},{"key":"9420_CR6","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1093\/imamat\/10.1.118","volume":"10","author":"A.R. Curtis","year":"1972","unstructured":"Curtis, A.R., Reid, J.K.: On the automatic scaling of matrices for Gaussian elimination. J. Inst. Math. Appl. 10, 118\u2013124 (1972)","journal-title":"J. Inst. Math. Appl."},{"key":"9420_CR7","volume-title":"Numerical Methods","author":"G. Dahlquist","year":"1963","unstructured":"Dahlquist, G., Bj\u00f6rck, \u00c5.: Numerical Methods. Prentice Hall, Englewood Cliffs (1963)"},{"key":"9420_CR8","first-page":"3","volume-title":"Proceedings of the Fourth International Conference on Operational Research","author":"J. Buchet de","year":"1966","unstructured":"de Buchet, J.: Experiments and statistical data on the solving of large-scale linear programs. In: Hertz, D.A., Melese, J. (eds.) Proceedings of the Fourth International Conference on Operational Research, pp.\u00a03\u201313. Wiley-Interscience, New York (1966)"},{"key":"9420_CR9","unstructured":"Elble, J.: Scaling linear programs: A comprehensive case study. Master\u2019s thesis, University of Illinois Urbana-Champaign, Urbana, IL (2007)"},{"key":"9420_CR10","unstructured":"Elble, J.M., Sahinidis, N.V.: Matrix binormalization on a GPU. In: Lecture Notes in Computer Science (2009, accepted)"},{"key":"9420_CR11","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1090\/S0002-9939-1955-0069585-4","volume":"6","author":"G.E. Forsythe","year":"1955","unstructured":"Forsythe, G.E., Straus, E.G.: On best conditioned matrices. Proc. Am. Math. Soc. 6, 340\u2013345 (1955)","journal-title":"Proc. Am. Math. Soc."},{"key":"9420_CR12","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1137\/1004032","volume":"4","author":"D.R. Fulkerson","year":"1962","unstructured":"Fulkerson, D.R., Wolfe, P.: An algorithm for scaling matrices. SIAM Rev. 4, 142\u2013146 (1962)","journal-title":"SIAM Rev."},{"key":"9420_CR13","volume-title":"Matrix Computations","author":"G.H. Golub","year":"1996","unstructured":"Golub, G.H., Van\u00a0Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)"},{"key":"9420_CR14","volume-title":"Introduction to Applied Numerical Analysis","author":"R.W. Hamming","year":"1971","unstructured":"Hamming, R.W.: Introduction to Applied Numerical Analysis. McGraw-Hill, New York (1971)"},{"key":"9420_CR15","unstructured":"IBM: IBM ILOG CPLEX Optimization Studio, Version 12.2 User\u2019s Manual, Armonk, NY (2010)"},{"key":"9420_CR16","first-page":"1","volume":"156","author":"J.A. Kelner","year":"2005","unstructured":"Kelner, J.A., Spielman, D.A.: A randomized polynomial-time simplex algorithm for linear programming (Preliminary version). Electron. Colloq. Comput. Complex. 156, 1\u201317 (2005)","journal-title":"Electron. Colloq. Comput. Complex."},{"key":"9420_CR17","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1080\/02331939308843895","volume":"27","author":"T. Larsson","year":"1993","unstructured":"Larsson, T.: On scaling linear programs\u2014Some experimental results. Optimization 27, 335\u2013373 (1993)","journal-title":"Optimization"},{"key":"9420_CR18","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1023\/B:NUMA.0000016606.32820.69","volume":"35","author":"O.E. Livne","year":"2004","unstructured":"Livne, O.E., Golub, G.H.: Scaling by binormalization. Numer. Algorithms 35, 97\u2013120 (2004)","journal-title":"Numer. Algorithms"},{"key":"9420_CR19","unstructured":"Makhorin, A.: GLPK\u2014GNU linear programming kit. http:\/\/www.gnu.org\/software\/glpk\/glpk.html (2008)"},{"key":"9420_CR20","unstructured":"Murtagh, B.A., Saunders, M.A.: MINOS 5.5 user\u2019s guide. Technical report, Department of Operations Research, Stanford University, Stanford, CA (1998)"},{"key":"9420_CR21","volume-title":"Advanced Linear Programming Computing Techniques","author":"W. Orchard-Hays","year":"1968","unstructured":"Orchard-Hays, W.: Advanced Linear Programming Computing Techniques. McGraw-Hill, New York (1968)"},{"key":"9420_CR22","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/TSMC.1987.289328","volume":"SMC-17","author":"D.A. Pierre","year":"1987","unstructured":"Pierre, D.A.: An optimal scaling method. IEEE Trans. Syst. Man Cybern. SMC-17, 2\u20136 (1987)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"9420_CR23","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/BF01581636","volume":"19","author":"U.G. Rothblum","year":"1980","unstructured":"Rothblum, U.G., Schneider, H.: Characterizations of optimal scalings of matrices. Math. Program. 19, 121\u2013136 (1980)","journal-title":"Math. Program."},{"key":"9420_CR24","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/BFb0120718","volume":"4","author":"J.A. Tomlin","year":"1975","unstructured":"Tomlin, J.A.: On scaling linear programming problems. Math. Program. Stud. 4, 146\u2013166 (1975)","journal-title":"Math. Program. Stud."},{"key":"9420_CR25","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF02165096","volume":"14","author":"A. Sluis van\u00a0der","year":"1969","unstructured":"van\u00a0der Sluis, A.: Condition numbers and equilibration of matrices. Numer. Math. 14, 14\u201323 (1969)","journal-title":"Numer. Math."},{"key":"9420_CR26","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1007\/BF02165662","volume":"15","author":"A. Sluis van\u00a0der","year":"1970","unstructured":"van\u00a0der Sluis, A.: Condition, equilibration and pivoting in linear algebraic systems. Numer. Math. 15, 74\u201386 (1970)","journal-title":"Numer. Math."},{"key":"9420_CR27","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/BF01396369","volume":"35","author":"M. Golitschek von","year":"1980","unstructured":"von Golitschek, M.: An algorithm for scaling matrices and computing the minimum cycle mean in a digraph. Numer. Math. 35, 45\u201355 (1980)","journal-title":"Numer. Math."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-011-9420-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-011-9420-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-011-9420-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:41Z","timestamp":1559288201000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-011-9420-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,13]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,6]]}},"alternative-id":["9420"],"URL":"https:\/\/doi.org\/10.1007\/s10589-011-9420-4","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,7,13]]}}}