{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,16]],"date-time":"2022-06-16T20:08:00Z","timestamp":1655410080698},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1998,3,1]],"date-time":"1998-03-01T00:00:00Z","timestamp":888710400000},"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":[[1998,3]]},"DOI":"10.1007\/bf01584845","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T08:36:57Z","timestamp":1114677417000},"page":"77-87","source":"Crossref","is-referenced-by-count":4,"title":["An interior point method, based on rank-1 updates, for linear programming"],"prefix":"10.1007","volume":"81","author":[{"given":"Jos F.","family":"Sturm","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuzhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N.K. Karmarkar","year":"1984","unstructured":"N.K. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373\u2013395.","journal-title":"Combinatorica"},{"key":"CR2","doi-asserted-by":"crossref","unstructured":"P.M. Vaidya, An algorithm for linear programming which requires O(((m + n)n 2 + (m + n)1.5n)L) arithmetic operations, Proceedings of the 19th ACM Symposium on the Theory of Computing, 1987, pp. 29\u201338.","DOI":"10.1145\/28395.28399"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4613-9617-8_1","volume-title":"Progress in Mathematical Programming","author":"C.C. Gonzaga","year":"1989","unstructured":"C.C. Gonzaga, An algorithm for solving linear programming problems in O(n 3L) operations, in: N. Megiddo (Ed.), Progress in Mathematical Programming, Springer, Berlin, 1989, pp. 1\u201328."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01587074","volume":"44","author":"M. Kojima","year":"1989","unstructured":"M. Kojima, S. Mizuno, A. Yoshise, A polynomial-time algorithm for a class of linear complementarity problems, Mathematical Programming 44 (1989) 1\u201326.","journal-title":"Mathematical Programming"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01587076","volume":"44","author":"R.D.C. Monteiro","year":"1989","unstructured":"R.D.C. Monteiro, I. Adler, Interior path following primal\u2014dual algorithms, Part II: convex quadratic programming, Mathematical Programming 44 (1989) 43\u201366.","journal-title":"Mathematical Programming"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF01580868","volume":"47","author":"K.M. Anstreicher","year":"1990","unstructured":"K.M. Anstreicher, A standard form variant, and safeguarded linesearch, for the modified Karmarkar algorithm, Mathematical Programming 47 (1990) 337\u2013351.","journal-title":"Mathematical Programming"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/BF01586053","volume":"54","author":"K.M. Anstreicher","year":"1992","unstructured":"K.M. Anstreicher, R.A. Bosch, Long steps in a O(n 3L) algorithm for linear programming, Mathematical Programming 54 (1992) 251\u2013265.","journal-title":"Mathematical Programming"},{"key":"CR8","volume-title":"Interior Point Approach to Linear, Quadratic and Convex Programming, Algorithms and Complexity","author":"D. Hertog Den","year":"1994","unstructured":"D. Den Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming, Algorithms and Complexity, Kluwer Academic Publishers, Dordrecht, 1994."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1137\/0802006","volume":"2","author":"D. Hertog Den","year":"1992","unstructured":"D. Den Hertog, C. Roos, J.-Ph. Vial, A complexity reduction for the long-step path-following algorithm for linear programming, SIAM Journal on Optimization 2 (1992) 71\u201387.","journal-title":"SIAM Journal on Optimization"},{"key":"CR10","unstructured":"Y. Ye, Further developments in potential reduction algorithm, Technical Report, Department of Management Sciences, University of Iowa, 1989."},{"key":"CR11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0024-3795(91)90273-Y","volume":"152","author":"S. Mizuno","year":"1991","unstructured":"S. Mizuno, \u201cO(n \u03c1L) iteration O(n 3L) potential reduction algorithms for linear programming, Linear Algebra and its Applications 152 (1991) 155\u2013168.","journal-title":"Linear Algebra and its Applications"},{"key":"CR12","first-page":"671","volume":"15","author":"S. Mizuno","year":"1990","unstructured":"S. Mizuno, A rank one updating algorithm for linear programming, The Arabian Journal for Science and Engineering 15 (1990) 671\u2013677.","journal-title":"The Arabian Journal for Science and Engineering"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1137\/0803044","volume":"3","author":"R.A. Bosch","year":"1993","unstructured":"R.A. Bosch, On Mizuno's rank one updating algorithm for linear programming, SIAM Journal on Optimization 3 (1993) 861\u2013867.","journal-title":"SIAM Journal on Optimization"},{"key":"CR14","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1287\/moor.15.3.508","volume":"15","author":"M.J. Todd","year":"1990","unstructured":"M.J. Todd, Y. Ye, A centered projective algorithm for linear programming, Mathematics of Operations Research 15 (1990) 508\u2013529.","journal-title":"Mathematics of Operations Research"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF01594937","volume":"50","author":"Y. Ye","year":"1991","unstructured":"Y. Ye, An O(n 3L) potential reduction algorithm for linear programming, Mathematical Programming 50 (1991) 239\u2013258.","journal-title":"Mathematical Programming"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1007\/BF01188712","volume":"9","author":"R.A. Bosch","year":"1993","unstructured":"R.A. Bosch, K.M. Anstreicher, On partial updating in a potential reduction linear programming algorithm of Kojima, Mizuno, and Yoshise, Algorithmica 9 (1993) 184\u2013197.","journal-title":"Mizuno, and Yoshise, Algorithmica"},{"key":"CR17","volume-title":"Deferred rank one updates in O(n 3L) interior point algorithms, Technical Report 90-11","author":"S. Mehrotra","year":"1990","unstructured":"S. Mehrotra, Deferred rank one updates in O(n 3L) interior point algorithms, Technical Report 90-11, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 1990."},{"key":"CR18","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF01580724","volume":"40","author":"J. Renegar","year":"1988","unstructured":"J. Renegar, A polynomial time algorithm, based on Newton's method, for linear programming, Mathematical Programming 40 (1988) 59\u201393.","journal-title":"Mathematical Programming"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF01580753","volume":"41","author":"D.F. Shanno","year":"1988","unstructured":"D.F. Shanno, Computing Karmarkar projections quickly, Mathematical Programming 41 (1988) 61\u201371.","journal-title":"Mathematical Programming"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01584845.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01584845\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01584845","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T03:46:46Z","timestamp":1586231206000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01584845"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,3]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,3]]}},"alternative-id":["BF01584845"],"URL":"https:\/\/doi.org\/10.1007\/bf01584845","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,3]]}}}