{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T15:00:19Z","timestamp":1726412419060},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1997,1,1]],"date-time":"1997-01-01T00:00:00Z","timestamp":852076800000},"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":[[1997,1]]},"DOI":"10.1007\/bf02614380","type":"journal-article","created":{"date-parts":[[2007,4,28]],"date-time":"2007-04-28T04:38:07Z","timestamp":1177735087000},"page":"117-130","source":"Crossref","is-referenced-by-count":4,"title":["Improved complexity using higher-order correctors for primal-dual Dikin affine scaling"],"prefix":"10.1007","volume":"76","author":[{"given":"B.","family":"Jansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Roos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Terlaky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Ye","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02614380_CR1","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1007\/BF02592024","volume":"36","author":"E.R. Barnes","year":"1986","unstructured":"E.R. Barnes, \u201cA variation on Karmarkar\u2019s algorithm for solving linear programming problems,\u201dMathematical Programming 36 (1986) 174\u2013182.","journal-title":"Mathematical Programming"},{"key":"BF02614380_CR2","first-page":"499","volume":"314","author":"D.A. Bayer","year":"1989","unstructured":"D.A. Bayer and J.C. Lagarias, \u201cThe nonlinear geometry of linear programming: I. Affine and projective scaling trajectories, II. Legendre transform coordinates and central trajectories,\u201dTransactions of the American Mathematical Society 314 (1989) 499\u2013581.","journal-title":"Transactions of the American Mathematical Society"},{"key":"BF02614380_CR3","first-page":"747","volume":"174","author":"I.I. Dikin","year":"1967","unstructured":"I.I. Dikin, \u201cIterative solution of problems of linear and quadratic programming,\u201dDoklady Akademiia Nauk SSSR 174 (1967) 747\u2013748.","journal-title":"Doklady Akademiia Nauk SSSR"},{"key":"BF02614380_CR4","first-page":"1","volume-title":"Progress in Mathematical Programming, Interior Point and Related Methods","author":"C.C. Gonzaga","year":"1988","unstructured":"C.C. Gonzaga, \u201cAn algorithm for solving linear programming programs in O(n 3L) operations,\u201d in N. Megiddo, ed.,Progress in Mathematical Programming, Interior Point and Related Methods (Springer, New York, 1988) pp. 1\u201328."},{"key":"BF02614380_CR5","series-title":"Working Paper","volume-title":"College of Business Administration","author":"P.-F. Hung","year":"1994","unstructured":"P.-F. Hung and Y. Ye, \u201cAn asymptotical $$O(\\sqrt n L)$$ -iteration path-following linear programming algorithm that uses long steps,\u201d Working Paper, College of Business Administration, The University of Iowa, Iowa City, IA (1994)."},{"key":"BF02614380_CR6","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1287\/moor.21.2.341","volume":"21","author":"B. Jansen","year":"1996","unstructured":"B. Jansen, C. Roos, and T. Terlaky, \u201cA polynomial primal-dual Dikin-type algorithm for linear programming,\u201dMathematics of Operations Research 21 (1996) 341\u2013353.","journal-title":"Mathematics of Operations Research"},{"key":"BF02614380_CR7","series-title":"Technical Report","volume-title":"A family of polynomial affine scaling algorithms for positive semi-definite linear complementarity problems","author":"B. Jansen","year":"1993","unstructured":"B. Jansen, C. Roos, and T. Terlaky, \u201cA family of polynomial affine scaling algorithms for positive semi-definite linear complementarity problems,\u201d Technical Report 93-112, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands (1993)."},{"key":"BF02614380_CR8","first-page":"29","volume-title":"Progress in Mathematical Programming, Interior Point and Related Methods","author":"M. Kojima","year":"1989","unstructured":"M. Kojima, S. Mizuno, and A. Yoshise, \u201cA primal-dual interior point algorithm for linear programming,\u201d in: N. Megiddo, ed.,Progress in Mathematical Programming, Interior Point and Related Methods (Springer, New York, 1989) pp. 29\u201347."},{"key":"BF02614380_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01587074","volume":"44","author":"M. Kojima","year":"1989","unstructured":"M. Kojima, S. Mizuno, and A. Yoshise, \u201cA polynomial-time algorithm for a class of linear complementarity problems,\u201dMathematical Programming 44 (1989) 1\u201326.","journal-title":"Mathematical Programming"},{"key":"BF02614380_CR10","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0024-3795(91)90275-2","volume":"152","author":"I.J. Lustig","year":"1991","unstructured":"I.J., Lustig, R.E. Marsten and D.F. Shanno, \u201cComputational experience with a primal-dual interior point method for linear programming\u201dLinear Algebra and its Applications 152 (1991) 191\u2013222.","journal-title":"Linear Algebra and its Applications"},{"key":"BF02614380_CR11","first-page":"131","volume-title":"Progress in Mathematical Programming. Interior Point and Related Methods","author":"N. Megiddo","year":"1988","unstructured":"N. Megiddo, \u201cPathways to the optimal set in linear programming,\u201d in N. Megiddo, ed.,Progress in Mathematical Programming. Interior Point and Related Methods (Springer, New York, 1988) pp. 131\u2013158."},{"key":"BF02614380_CR12","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1137\/0802028","volume":"2","author":"S. Mehrotra","year":"1992","unstructured":"S. Mehrotra, \u201cOn the implementation of a (primal-dual) interior point method.\u201dSIAM Journal on Optimization 2 (1992) 575\u2013601.","journal-title":"SIAM Journal on Optimization"},{"key":"BF02614380_CR13","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF01587075","volume":"44","author":"R.C. Monteiro","year":"1989","unstructured":"R.C. Monteiro and I. Adler, \u201cInterior path following primal-dual algorithms. Part I: Linear programming,\u201dMathematical Programming 44 (1989) 27\u201342.","journal-title":"Mathematical Programming"},{"key":"BF02614380_CR14","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1287\/moor.15.2.191","volume":"15","author":"R.C. Monteiro","year":"1990","unstructured":"R.C. Monteiro, I. Adler and M.G.C. Resende, \u201cA polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension,\u201dMathematics of Operations Research 15 (1990) 191\u2013214.","journal-title":"Mathematics of Operations Research"},{"key":"BF02614380_CR15","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1287\/moor.18.4.964","volume":"18","author":"S. Mizuno","year":"1993","unstructured":"S. Mizuno, M.J. Todd, and Y. Ye, \u201cOn adaptive-step primal-dual interior-point algorithms for linear programming.\u201dMathematics of Operations Research 18 (1993) 964\u2013981.","journal-title":"Mathematics of Operations Research"},{"key":"BF02614380_CR16","first-page":"433","volume-title":"Economic Decision Making: Games, Economics and Optimization","author":"C. Roos","year":"1989","unstructured":"C. Roos and J.-Ph. Vial, \u201cLong steps with the logarithmic penalty barrier function in linear programming,\u201d in: J. Gabszeywicz, J.F. Richard, and L. Wolsey, eds.,Economic Decision Making: Games, Economics and Optimization (Elsevier Science Publishers, Amsterdam, 1989) pp. 433\u2013441."},{"key":"BF02614380_CR17","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF01580724","volume":"40","author":"J. Renegar","year":"1988","unstructured":"J. Renegar, \u201cA polynomial-time algorithm based on Newton\u2019s method for linear programming,\u201dMathematical Programming 40 (1988) 59\u201394.","journal-title":"Mathematical Programming"},{"key":"BF02614380_CR18","series-title":"Lecture Notes in Control and Information Sciences, Vol.","first-page":"866","volume-title":"An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming","author":"G. Sonnevend","year":"1985","unstructured":"G. Sonnevend, \u201cAn analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming,\u201d in:Lecture Notes in Control and Information Sciences, Vol. 84 (Springer, New York, 1985) pp. 866\u2013876."},{"key":"BF02614380_CR19","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/BF01840454","volume":"1","author":"R.J. Vanderbei","year":"1986","unstructured":"R.J. Vanderbei, M.S. Meketon and B.A. Freedman, \u201cA modification of Karmarkar\u2019s linear programming algorithm.\u201dAlgorithmica 1 (1986) 395\u2013407.","journal-title":"Algorithmica"},{"key":"BF02614380_CR20","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1287\/moor.19.1.53","volume":"19","author":"Y. Ye","year":"1994","unstructured":"Y. Ye, M.J. Todd, and S. Mizuno, \u201cAn $$O(\\sqrt n L)$$ -iteration homogeneous and self-dual linear programming algorithm,\u201dMathematics of Operations Research 19 (1994) 53\u201367.","journal-title":"Mathematics of Operations Research"},{"key":"BF02614380_CR21","series-title":"Technical Report","volume-title":"On polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms","author":"L. Zhang","year":"1993","unstructured":"L. Zhang and Y. Zhang, \u201cOn polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms,\u201d Technical Report 93-12, Department of Mathematics and Statistics, University of Maryland at Baltimore County, Baltimore, MD (1993)."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02614380.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02614380\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02614380","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T08:49:25Z","timestamp":1558342165000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02614380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["BF02614380"],"URL":"https:\/\/doi.org\/10.1007\/bf02614380","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}