{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T18:33:23Z","timestamp":1759602803776},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1982,12,1]],"date-time":"1982-12-01T00:00:00Z","timestamp":407548800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1982,12]]},"DOI":"10.1007\/bf01583778","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T08:31:20Z","timestamp":1114677080000},"page":"34-49","source":"Crossref","is-referenced-by-count":23,"title":["An implementation of the simplex method for linear programming problems with variable upper bounds"],"prefix":"10.1007","volume":"23","author":[{"given":"Michael J.","family":"Todd","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1007\/BF02169151","volume":"16","author":"R.H. Bartels","year":"1971","unstructured":"R.H. Bartels, \u201cA stabilization of the simplex method\u201d,Numerische Mathematik 16 (1971) 414\u2013434.","journal-title":"Numerische Mathematik"},{"key":"CR2","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1145\/362946.362974","volume":"12","author":"R.H. Bartels","year":"1969","unstructured":"R.H. Bartels and G.H. Golub, \u201cThe simplex method for linear programming usingLU decomposition\u201d,Communications of the ACM 12 (1969) 266\u2013268.","journal-title":"Communications of the ACM"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/B978-0-12-597050-1.50009-9","volume-title":"Nonlinear programming","author":"R.H. Bartels","year":"1970","unstructured":"R.H. Bartels, G.H. Golub and M.A. Saunders, \u201cNumerical techniques in mathematical programming\u201d, in: J. Rosen, O. Mangasarian and K. Ritter, eds.,Nonlinear programming (Academic Press, New York, 1970) pp. 123\u2013176."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01609039","volume":"15","author":"R.C. Daniel","year":"1978","unstructured":"R.C. Daniel, \u201cA note on Schrage's generalized variable upper bounds\u201d,Mathematical Programming 15 (1978) 349\u2013351.","journal-title":"Mathematical Programming"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1287\/opre.22.3.478","volume":"22","author":"R. Dutton","year":"1974","unstructured":"R. Dutton, G. Hinman and C.B. Millham, \u201cThe optimal location of nuclear-power facilities in the Pacific Northwest\u201d,Operations Research 22 (1974) 478\u2013487.","journal-title":"Operations Research"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01584548","volume":"2","author":"J.J.H. Forest","year":"1972","unstructured":"J.J.H. Forest and J.A. Tomlin, \u201cUpdating triangular factors of the basis to maintain sparsity in the product form of the simplex method\u201d,Mathematical Programming 2 (1972) 263\u2013278.","journal-title":"Mathematical Programming"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0024-3795(73)90047-5","volume":"7","author":"P. Gill","year":"1973","unstructured":"P. Gill and W. Murray, \u201cA numerically stable form of the simplex algorithm\u201d,Journal of Linear Algebra and its Applications 7 (1973) 99\u2013138.","journal-title":"Journal of Linear Algebra and its Applications"},{"key":"CR8","first-page":"1051","volume":"29","author":"P. Gill","year":"1975","unstructured":"P. Gill, W. Murray and M.A. Saunders, \u201cMethods for computing and modifying the LDV factors of a matrix\u201d,Mathematics of Computation 29 (1975) 1051\u20131077.","journal-title":"Mathematics of Computation"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1007\/BF01593773","volume":"12","author":"F. Glover","year":"1977","unstructured":"F. Glover, \u201cCompact LP bases for a class of IP problems\u201d,Mathematical Programming 12 (1977) 102\u2013109.","journal-title":"Mathematical Programming"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1007\/BF01584343","volume":"13","author":"D. Goldfarb","year":"1977","unstructured":"D. Goldfarb, \u201cOn the Bartels-Golub decomposition for linear programming bases\u201d,Mathematical Programming 13 (1977) 272\u2013279.","journal-title":"Mathematical Programming"},{"key":"CR11","unstructured":"G. Roodman and L. Schwartz, \u201cThe dynamic plant location problem\u201d, working paper, University of Rochester (1974)."},{"key":"CR12","volume-title":"\u201cLarge-scale programming using the Cholesky factorization\u201d, Report Stan-CS-72252","author":"M.A. Saunders","year":"1972","unstructured":"M.A. Saunders, \u201cLarge-scale programming using the Cholesky factorization\u201d, Report Stan-CS-72252, Computer Science Department, Stanford University (Stanford, 1972)."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1007\/BFb0120715","volume":"4","author":"L. Schrage","year":"1975","unstructured":"L. Schrage, \u201cImplicit representation of variable upper bounds in linear programming\u201d,Mathematical Programming Study 4 (1975) 118\u2013132.","journal-title":"Mathematical Programming Study"},{"key":"CR14","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01588948","volume":"14","author":"L. Schrage","year":"1978","unstructured":"L. Schrage, \u201cImplicit representation of generalized variable upper bounds in linear programming\u201d,Mathematical Programming 14 (1978) 11\u201320.","journal-title":"Mathematical Programming"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1287\/moor.5.2.242","volume":"5","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd, \u201cTraversing large pieces of linearity in algorithms that solve equations by following piecewise-linear paths\u201d,Mathematics of Operations Research 5 (1980) 242\u2013257.","journal-title":"Mathematics of Operations Research"},{"key":"CR16","first-page":"1","volume-title":"Analysis and computation of fixed points","author":"M.J. Todd","year":"1980","unstructured":"M.J. Todd, \u201cNumerical stability and sparsity in piecewise-linear algorithms\u201d, in: S.M. Robinson, ed.,Analysis and computation of fixed points (Academic Press, New York, 1980) pp. 1\u201324."},{"key":"CR17","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1137\/1007004","volume":"7","author":"P. Wolfe","year":"1965","unstructured":"P. Wolfe, \u201cThe composite simplex algorithm\u201d,SIAM Review 7 (1965) 42\u201354.","journal-title":"SIAM Review"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/BFb0120693","volume":"2","author":"H.P. Williams","year":"1974","unstructured":"H.P. Williams, \u201cExperiments in the formulation of integer programming problems\u201d,Mathematical Programming Study 2 (1974) 180\u2013197.","journal-title":"Mathematical Programming Study"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01583778.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01583778\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01583778","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:29:24Z","timestamp":1556897364000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01583778"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["BF01583778"],"URL":"https:\/\/doi.org\/10.1007\/bf01583778","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}