{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:45:49Z","timestamp":1751874349273},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1-6","license":[{"start":{"date-parts":[[1991,6,1]],"date-time":"1991-06-01T00:00:00Z","timestamp":675734400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithmica"],"published-print":{"date-parts":[[1991,6]]},"DOI":"10.1007\/bf01759039","type":"journal-article","created":{"date-parts":[[2005,6,16]],"date-time":"2005-06-16T06:43:56Z","timestamp":1118904236000},"page":"153-181","source":"Crossref","is-referenced-by-count":17,"title":["Search directions for interior linear-programming methods"],"prefix":"10.1007","volume":"6","author":[{"given":"Clovis C.","family":"Gonzaga","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF01759039_CR1","series-title":"Report ORC86-8","volume-title":"An Implementation of Karmarkar's Algorithm for Linear Programming","author":"I. Adler","year":"1986","unstructured":"I. Adler, M. Resende, and G. Veiga. An Implementation of Karmarkar's Algorithm for Linear Programming. Report ORC86-8, Operations Research Center, University of California, Berkeley, May 1986."},{"key":"BF01759039_CR2","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/BF01840458","volume":"1","author":"K. Anstreicher","year":"1986","unstructured":"K. Anstreicher. A monotonic projective algorithm for fractional linear programming.Algorithmica,1:483\u2013498, 1986.","journal-title":"Algorithmica"},{"key":"BF01759039_CR3","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1007\/BF02592024","volume":"36","author":"E. R. Barnes","year":"1986","unstructured":"E. R. Barnes. A variation on Karmarkar's algorithm for solving linear programming problems.Mathematical Programming,36:174\u2013182, 1986.","journal-title":"Mathematical Programming"},{"key":"BF01759039_CR4","volume-title":"Manuscript in preparation","author":"E. R. Barnes","year":"1987","unstructured":"E. R. Barnes and D. L. Jensen. A Polynomial-Time Version of the Affine-Scaling Algorithm. Manuscript in preparation, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1987."},{"key":"BF01759039_CR5","volume-title":"Karmarkar's Linear Programming Algorithm and Newton's Method","author":"K. Bayer","year":"1986","unstructured":"K. Bayer and J. C. Lagarias. Karmarkar's Linear Programming Algorithm and Newton's Method. Preprints, AT&T Bell Laboratories, Murray Hill, NJ, 1986."},{"key":"BF01759039_CR6","unstructured":"T. Cavalier and A. Soyster. Some Computational Experience and a Modification of the Karmarkar Algorithm. Working Paper 85\u2013105, Department of Industrial and Management System Engineering, Pennsylvania State University, February 1985."},{"key":"BF01759039_CR7","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0717023","volume":"17","author":"W. C. Davidon","year":"1980","unstructured":"W. C. Davidon. Conic approximations and collinear scalings for optimizers.SIAM Journal on Numerical Analysis,17:268\u2013281, 1980.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"BF01759039_CR8","volume-title":"Nonlinear Programming: Sequential Unconstrained Minimization Techniques","author":"A. Fiacco","year":"1955","unstructured":"A. Fiacco and G. McCormick. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York, 1955."},{"key":"BF01759039_CR9","volume-title":"Memorandum","author":"K. R. Frisch","year":"1955","unstructured":"K. R. Frisch. The Logarithmic Potential Method of Convex Programming. Memorandum, University Institute of Economics, Oslo, May 1955."},{"key":"BF01759039_CR10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF02591685","volume":"37","author":"D. Gay","year":"1987","unstructured":"D. Gay. A variant of Karmarkar's linear programming algorithm for problems in standard form.Mathematical Programming,37:81\u201389, 1987.","journal-title":"Mathematical Programming"},{"key":"BF01759039_CR11","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF02592025","volume":"36","author":"P. Gill","year":"1986","unstructured":"P. Gill, W. Murray, M. Saunders, J. Tomlin, and M. Wright. On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method.Mathematical Programming,36:183\u2013209, 1986.","journal-title":"Mathematical Programming"},{"key":"BF01759039_CR12","series-title":"Memorandum UCB\/ERL M85\/61","volume-title":"A Conical Projection Algorithm for Linear Programming","author":"C. Gonzaga","year":"1985","unstructured":"C. Gonzaga. A Conical Projection Algorithm for Linear Programming. Memorandum UCB\/ERL M85\/61, Electronics Research Laboratory, University of California, Berkeley, CA, July 1985."},{"key":"BF01759039_CR13","series-title":"Memorandum UCB\/ERL M87\/10","volume-title":"An Algorithm for Solving Linear Programming Problems inO(n 3 L) operations","author":"C. Gonzaga","year":"1987","unstructured":"C. Gonzaga. An Algorithm for Solving Linear Programming Problems inO(n 3 L) operations. Memorandum UCB\/ERL M87\/10, Electronics Research Laboratory, University of California, Berkeley, CA, March 1987."},{"key":"BF01759039_CR14","series-title":"Memorandum UCB\/ERL M87\/11","volume-title":"Conical Projection Algorithms for Linear Programming","author":"C. Gonzaga","year":"1987","unstructured":"C. Gonzaga. Conical Projection Algorithms for Linear Programming. Memorandum UCB\/ERL M87\/11, Electronics Research Laboratory, University of California, Berkeley, CA, March 1987. To appear inMathematical Programming."},{"key":"BF01759039_CR15","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF01580721","volume":"40","author":"H. Imai","year":"1988","unstructured":"H. Imai. On the convexity of the multiplicative version of Karmarkar's potential function.Mathematical Programming,40:29\u201332, 1988.","journal-title":"Mathematical Programming"},{"key":"BF01759039_CR16","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/BF01840457","volume":"1","author":"M. Iri","year":"1986","unstructured":"M. Iri and H. Imai. A multiplicative penalty function method for linear programming.Algorithmica,1:455\u2013482, 1986.","journal-title":"Algorithmica"},{"key":"BF01759039_CR17","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N. Karmarkar","year":"1984","unstructured":"N. Karmarkar. A new polynomial time algorithm for linear programming.Combinatorica,4:373\u2013395, 1984.","journal-title":"Combinatorica"},{"key":"BF01759039_CR18","unstructured":"J. C. Lagarias. Personal communication."},{"key":"BF01759039_CR19","series-title":"Research Report RJ 5295","volume-title":"Pathways to the Optimal Set in Linear Programming","author":"N. Megiddo","year":"1986","unstructured":"N. Megiddo. Pathways to the Optimal Set in Linear Programming. Research Report RJ 5295, IBM Almaden Research Center, San Jose, CA, 1986."},{"key":"BF01759039_CR20","volume-title":"Manuscript","author":"M. Padberg","year":"1985","unstructured":"M. Padberg. Solution of a Nonlinear Programming Problem Arising in the Projective Method for Linear Programming. Manuscript, New York University, New York, March 1985."},{"key":"BF01759039_CR21","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,40:59\u201394, 1988.","journal-title":"Mathematical Programming"},{"key":"BF01759039_CR22","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/BF01840455","volume":"1","author":"M. Todd","year":"1986","unstructured":"M. Todd and B. Burrell. An extension of Karmarkar's algorithm for linear programming using dual variables.Algorithmica,1:409\u2013424, 1986.","journal-title":"Algorithmica"},{"key":"BF01759039_CR23","volume-title":"An Algorithm for Linear Programming which RequiresO(((m+n)n 2+(m+n)1.5 n)L) Arithmetic Operations","author":"P. M. Vaidya","year":"1987","unstructured":"P. M. Vaidya. An Algorithm for Linear Programming which RequiresO(((m+n)n 2+(m+n)1.5 n)L) Arithmetic Operations. Preprint, AT&T Bell Laboratories, Murray Hill, NJ, 1987."},{"key":"BF01759039_CR24","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/BF01840454","volume":"1","author":"R. J. Vanderbei","year":"1986","unstructured":"R. J. Vanderbei, M. J. Meketon, and B. A. Freedman. A modification of Karmarkar's linear programming algorithm.Algorithmica,1:395\u2013407, 1986.","journal-title":"Algorithmica"},{"key":"BF01759039_CR25","volume-title":"Manuscript","author":"H. Yamashita","year":"1986","unstructured":"H. Yamashita. A Polynomially and Quadratically Convergent Method for Linear Programming. Manuscript, Mathematical Systems Institute Inc., Tokyo, October 1986."}],"container-title":["Algorithmica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01759039.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01759039\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01759039","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T12:25:43Z","timestamp":1557318343000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01759039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":25,"journal-issue":{"issue":"1-6","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["BF01759039"],"URL":"https:\/\/doi.org\/10.1007\/bf01759039","relation":{},"ISSN":["0178-4617","1432-0541"],"issn-type":[{"value":"0178-4617","type":"print"},{"value":"1432-0541","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}