{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,10,23]],"date-time":"2022-10-23T19:27:40Z","timestamp":1666553260071},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1992,8,1]],"date-time":"1992-08-01T00:00:00Z","timestamp":712627200000},"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":[[1992,8]]},"DOI":"10.1007\/bf01580904","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T04:58:11Z","timestamp":1114664291000},"page":"301-319","source":"Crossref","is-referenced-by-count":34,"title":["On the convergence of the affine-scaling algorithm"],"prefix":"10.1007","volume":"56","author":[{"given":"Paul","family":"Tseng","sequence":"first","affiliation":[]},{"given":"Zhi-Quan","family":"Luo","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1287\/ijoc.1.2.84","volume":"1","author":"I. Adler","year":"1989","unstructured":"I. Adler, N. Karmarkar, M.G.C. Resende and G. Veiga, \u201cData structures and programming techniques for the implementation of Karmarkar's algorithm,\u201dORSA Journal on Computing 1 (1989) 84\u2013106.","journal-title":"ORSA Journal on Computing"},{"key":"CR2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF01594923","volume":"50","author":"I. Adler","year":"1991","unstructured":"I. Adler and R.D.C. Monteiro, \u201cLimiting behavior of the affine scaling continuous trajectories for linear programming problems,\u201dMathematical Programming 50 (1991) 29\u201351.","journal-title":"Mathematical Programming"},{"key":"CR3","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's algorithm for solving linear programming problems,\u201dMathematical Programming 36 (1986) 174\u2013182.","journal-title":"Mathematical Programming"},{"key":"CR4","volume-title":"Parallel and Distributed Computation: Numerical Methods","author":"D.P. Bertsekas","year":"1989","unstructured":"D.P. Bertsekas and J.N. Tsitsiklis,Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1989)."},{"key":"CR5","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01589405","volume":"42","author":"D.P. Bertsekas","year":"1988","unstructured":"D.P. Bertsekas and J. Eckstein, \u201cDual coordinate step methods for linear network flow problems,\u201dMathematical Programming 42 (1988) 203\u2013243.","journal-title":"Mathematical Programming"},{"key":"CR6","series-title":"ISME Working Paper","volume-title":"Some computational experience and a modification of Karmarkar's algorithm","author":"T.M. Cavalier","year":"1985","unstructured":"T.M. Cavalier and A.L. Soyster, \u201cSome computational experience and a modification of Karmarkar's algorithm,\u201d ISME Working Paper 85-105, Pennsylvania State University (University Park, PA, 1985)."},{"key":"CR7","series-title":"Research Memorandum","volume-title":"A class of algorithms for linear programming","author":"V. Chandru","year":"1985","unstructured":"V. Chandru and B.S. Kochar, \u201cA class of algorithms for linear programming,\u201d Research Memorandum No. 85-14, Purdue University (Lafayette, IN, 1985)."},{"key":"CR8","series-title":"Research Memorandum","volume-title":"Exploring special structures using a variant of Karmarkar's algorithm","author":"V. Chandru","year":"1986","unstructured":"V. Chandru and B.S. Kochar, \u201cExploring special structures using a variant of Karmarkar's algorithm,\u201d Research Memorandum No. 86-10, Purdue University (Lafayette, IN, 1986)."},{"key":"CR9","first-page":"674","volume":"8","author":"I.I. Dikin","year":"1967","unstructured":"I.I. Dikin, \u201cIterative solution of problems of linear and quadratic programming,\u201dSoviet Mathematics Doklady 8 (1967) 674\u2013675.","journal-title":"Soviet Mathematics Doklady"},{"key":"CR10","first-page":"54","volume":"12","author":"I.I. Dikin","year":"1974","unstructured":"I.I. Dikin, \u201cOn the speed of an iterative process,\u201dUpravlyaemye Sistemi 12 (1974) 54\u201360.","journal-title":"Upravlyaemye Sistemi"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/BF01580777","volume":"41","author":"I.I. Dikin","year":"1988","unstructured":"I.I. Dikin, Letter to the Editor,Mathematical Programming 41 (1988) 393\u2013394.","journal-title":"Mathematical Programming"},{"key":"CR12","volume-title":"Flows in Networks","author":"L.R. Ford","year":"1962","unstructured":"L.R. Ford and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, NJ, 1962)."},{"key":"CR13","volume-title":"\u201cThe logarithmic potential method of convex programming,\u201d Technical Report","author":"K.R. Frisch","year":"1955","unstructured":"K.R. Frisch, \u201cThe logarithmic potential method of convex programming,\u201d Technical Report. University Institute of Economics (Oslo, Norway, 1955)."},{"key":"CR14","volume-title":"Progress in Mathematical Programming: Interior-Point and Related Methods","author":"C.C. Gonzaga","year":"1989","unstructured":"C.C. Gonzaga, \u201cAn algorithm for solving linear programming problems in O(n 3 L) operations,\u201d in: N. Megiddo, ed.,Progress in Mathematical Programming: Interior-Point and Related Methods (Springer, New York, 1989)."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"A.J. Hoffman","year":"1952","unstructured":"A.J. Hoffman, \u201cOn approximate solutions of systems of linear inequalities,\u201dJournal of Research of the National Bureau of Standards 49 (1952) 263\u2013265.","journal-title":"Journal of Research of the National Bureau of Standards"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N. Karmarkar","year":"1984","unstructured":"N. Karmarkar, \u201cA new polynomial-time algorithm for linear programming,\u201dCombinatorica 4 (1984) 373\u2013395.","journal-title":"Combinatorica"},{"key":"CR17","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":"CR18","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0377-2217(87)90270-0","volume":"32","author":"K.O. Kortanek","year":"1987","unstructured":"K.O. Kortanek and M. Shi, \u201cConvergence results and numerical experiments on a linear programming hybrid algorithm,\u201dEuropean Journal of Operational Research 32 (1987) 47\u201361.","journal-title":"European Journal of Operational Research"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1137\/0325033","volume":"25","author":"O.L. Mangasarian","year":"1987","unstructured":"O.L. Mangasarian and T.-H. Shiau, \u201cLipschitz continuity of solutions of linear inequalities, programs and complementarity problems,\u201dSIAM Journal on Control and Optimization 25 (1987) 583\u2013595.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"CR20","series-title":"Working Paper","volume-title":"Implementation of a dual affine interior point algorithm for linear programming","author":"R.E. Marsten","year":"1988","unstructured":"R.E. Marsten, M.J. Saltzman, D.F. Shanno and G.S. Pierece, \u201cImplementation of a dual affine interior point algorithm for linear programming,\u201d Working Paper, Center for the Management of Information, University of Arizona (Tucson, AZ, 1988)."},{"key":"CR21","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1287\/moor.14.1.97","volume":"14","author":"N. Megiddo","year":"1989","unstructured":"N. Megiddo and M. Shub, \u201cBoundary behavior of interior point algorithms in linear programming,\u201dMathematics of Operations Research 14 (1989) 97\u2013146.","journal-title":"Mathematics of Operations Research"},{"key":"CR22","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1137\/0728029","volume":"28","author":"S. Mehrotra","year":"1991","unstructured":"S. Mehrotra and J. Sun, \u201cA method of analytic centers for quadratically constrained convex quadratic programs,\u201dSIAM Journal on Numerical Analysis 28 (1991) 529\u2013544.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"CR23","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0167-6377(87)90040-X","volume":"6","author":"C.L. Monma","year":"1987","unstructured":"C.L. Monma and A.J. Morton, \u201cComputational experiments with a dual affine variant of Karmarkar's method for linear programming,\u201dOperations Research Letters 6 (1987) 261\u2013267.","journal-title":"Operations Research Letters"},{"key":"CR24","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01587076","volume":"44","author":"R.C. Monteiro","year":"1989","unstructured":"R.C. Monteiro and I. Adler, \u201cInterior path following primal-dual algorithms. Part II: convex quadratic programming,\u201dMathematical Programming 44 (1989) 43\u201366.","journal-title":"Mathematical Programming"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1287\/moor.15.2.191","volume":"15","author":"R.D.C. Monteiro","year":"1990","unstructured":"R.D.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":"CR26","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"J.M. Ortega","year":"1970","unstructured":"J.M. Ortega and W.C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970)."},{"key":"CR27","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"C.H. Papadimitriou","year":"1982","unstructured":"C.H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, NJ, 1982)."},{"key":"CR28","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/0022-247X(79)90234-8","volume":"72","author":"G.B. Passty","year":"1979","unstructured":"G.B. Passty, \u201cErgodic convergence to a zero of the sum of monotone operators in Hilbert space,\u201dJournal of Mathematical Analysis and its Applications 72 (1979) 383\u2013390.","journal-title":"Journal of Mathematical Analysis and its Applications"},{"key":"CR29","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's method, for linear programming,\u201dMathematical Programming 40 (1988) 59\u201393.","journal-title":"Mathematical Programming"},{"key":"CR30","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0024-3795(73)90007-4","volume":"6","author":"S.M. Robinson","year":"1973","unstructured":"S.M. Robinson, \u201cBounds for errors in the solution set of a perturbed linear program,\u201dLinear Algebra and its Applications 6 (1973) 69\u201381.","journal-title":"Linear Algebra and its Applications"},{"key":"CR31","volume-title":"Network Flows and Monotropic Optimization","author":"R.T. Rockafellar","year":"1984","unstructured":"R.T. Rockafellar,Network Flows and Monotropic Optimization (Wiley, New York, 1984)."},{"key":"CR32","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01585708","volume":"53","author":"P. Tseng","year":"1992","unstructured":"P. Tseng, \u201cComplexity analysis of a linear complementarity algorithm based on a Lyapunov function,\u201dMathematical Programming 53 (1992) 297\u2013306.","journal-title":"Mathematical Programming"},{"key":"CR33","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1287\/moor.12.4.569","volume":"12","author":"P. Tseng","year":"1987","unstructured":"P. Tseng and D.P. Bertsekas, \u201cRelaxation methods for linear programs,\u201dMathematics of Operations Research 12 (1987) 569\u2013596.","journal-title":"Mathematics of Operations Research"},{"key":"CR34","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF01585734","volume":"46","author":"P. Tseng","year":"1990","unstructured":"P. Tseng and D.P. Bertsekas, \u201cRelaxation methods for monotropic programs,\u201dMathematical Programming 46 (1990) 127\u2013151.","journal-title":"Mathematical Programming"},{"key":"CR35","unstructured":"T. Tsuchiya, \u201cGlobal convergence property of the affine scaling methods for primal degenerate linear programming problems,\u201d to appear in:Mathematics of Operations Research."},{"key":"CR36","volume-title":"\u201cGlobal convergence of the affine scaling methods for degenerate linear programming problems,\u201d Technical Report","author":"T. Tsuchiya","year":"1990","unstructured":"T. Tsuchiya, \u201cGlobal convergence of the affine scaling methods for degenerate linear programming problems,\u201d Technical Report, The Institute of Statistical Mathematics (Tokyo, Japan, 1990)."},{"key":"CR37","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF01580859","volume":"47","author":"P.M. Vaidya","year":"1990","unstructured":"P.M. Vaidya, \u201cAn algorithm for linear programming which requires O(((m+n)n 2 +(m+n) 1.5 n)L) arithmetic operations,\u201dMathematical Programming 47 (1990) 175\u2013201.","journal-title":"Mathematical Programming"},{"key":"CR38","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF01582276","volume":"43","author":"R.J. Vanderbei","year":"1989","unstructured":"R.J. Vanderbei, \u201cAffine-scaling for linear programs with free variables,\u201dMathematical Programming 43 (1989) 31\u201344.","journal-title":"Mathematical Programming"},{"key":"CR39","volume-title":"\u201cI.I. Dikin's convergence result for the affine-scaling algorithm,\u201d Technical Report","author":"R.J. Vanderbei","year":"1988","unstructured":"R.J. Vanderbei and J.C. Lagarias, \u201cI.I. Dikin's convergence result for the affine-scaling algorithm,\u201d Technical Report, AT&T Bell Laboratories (Murray Hill, NJ, 1988)."},{"key":"CR40","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. Freeman, \u201cA modification of Karmarkar's linear programming algorithm,\u201dAlgorithmica 1 (1986) 395\u2013407.","journal-title":"Algorithmica"},{"key":"CR41","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF01594937","volume":"50","author":"Y. Ye","year":"1991","unstructured":"Y. Ye, \u201cAn O(n 3 L) potential reduction algorithm for linear programming,\u201dMathematical Programming 50 (1991) 239\u2013258.","journal-title":"Mathematical Programming"},{"key":"CR42","volume-title":"Progress in Mathematical Programming: Interior-Point and Related Methods","author":"Y. Ye","year":"1989","unstructured":"Y. Ye, \u201cAn extension of Karmarkar's algorithm and the trust region method for quadratic programming,\u201d in: N. Megiddo, ed.,Progress in Mathematical Programming: Interior-Point and Related Methods (Springer, New York, 1989)."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580904.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01580904\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580904","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T11:12:12Z","timestamp":1556881932000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01580904"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,8]]},"references-count":42,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1992,8]]}},"alternative-id":["BF01580904"],"URL":"http:\/\/dx.doi.org\/10.1007\/bf01580904","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":["General Mathematics","Software"],"published":{"date-parts":[[1992,8]]}}}