An implementation of Karmarkar's algorithm for linear programming
 Ilan Adler,
 Mauricio G. C. Resende,
 Geraldo Veiga,
 Narendra Karmarkar
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This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested. Linear programs are expressed in an inequality form, which allows for the inexact computation of the algorithm's direction of improvement, resulting in a significant computational advantage. Implementation issues particular to this family of algorithms, such as treatment of dense columns, are discussed. The code is tested on several standard linear programming problems and compares favorably with the simplex codeMinos 4.0.
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 Title
 An implementation of Karmarkar's algorithm for linear programming
 Journal

Mathematical Programming
Volume 44, Issue 13 , pp 297335
 Cover Date
 19890501
 DOI
 10.1007/BF01587095
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Linear programming
 Karmarkar's algorithm
 interior point methods
 Industry Sectors
 Authors

 Ilan Adler ^{(1)}
 Mauricio G. C. Resende ^{(1)}
 Geraldo Veiga ^{(1)}
 Narendra Karmarkar ^{(2)}
 Author Affiliations

 1. Department of Industrial Engineering and Operations Research, University of California, 94720, Berkeley, CA, USA
 2. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA