Mathematical Programming

, Volume 44, Issue 1, pp 297–335

An implementation of Karmarkar's algorithm for linear programming

  • Ilan Adler
  • Mauricio G. C. Resende
  • Geraldo Veiga
  • Narendra Karmarkar
Article

DOI: 10.1007/BF01587095

Cite this article as:
Adler, I., Resende, M.G.C., Veiga, G. et al. Mathematical Programming (1989) 44: 297. doi:10.1007/BF01587095

Abstract

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.

Key words

Linear programming Karmarkar's algorithm interior point methods 

Copyright information

© The Mathematical Programming Society, Inc. 1989

Authors and Affiliations

  • Ilan Adler
    • 1
  • Mauricio G. C. Resende
    • 1
  • Geraldo Veiga
    • 1
  • Narendra Karmarkar
    • 2
  1. 1.Department of Industrial Engineering and Operations ResearchUniversity of CaliforniaBerkeleyUSA
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

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