Algorithmica

, Volume 1, Issue 1, pp 395–407

A modification of karmarkar's linear programming algorithm

Authors

  • Robert J. Vanderbei
    • AT&T Bell Laboratories
  • Marc S. Meketon
    • AT&T Bell Laboratories
  • Barry A. Freedman
    • AT&T Bell Laboratories
Article

DOI: 10.1007/BF01840454

Cite this article as:
Vanderbei, R.J., Meketon, M.S. & Freedman, B.A. Algorithmica (1986) 1: 395. doi:10.1007/BF01840454

Abstract

We present a modification of Karmarkar's linear programming algorithm. Our algorithm uses a recentered projected gradient approach thereby obviatinga priori knowledge of the optimal objective function value. Assuming primal and dual nondegeneracy, we prove that our algorithm converges. We present computational comparisons between our algorithm and the revised simplex method. For small, dense constraint matrices we saw little difference between the two methods.

Key words

Linear programming Karmarkar's algorithm Projected gradient methods Least squares

Copyright information

© Springer-Verlag New York Inc. 1986