Mathematical Programming

, Volume 44, Issue 1, pp 27–41

Interior path following primal-dual algorithms. part I: Linear programming

  • Renato D. C. Monteiro
  • Ilan Adler

DOI: 10.1007/BF01587075

Cite this article as:
Monteiro, R.D.C. & Adler, I. Mathematical Programming (1989) 44: 27. doi:10.1007/BF01587075


We describe a primal-dual interior point algorithm for linear programming problems which requires a total of\(O\left( {\sqrt n L} \right)\) number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea.

Key words

Interior-point methods linear programming Karmarkar's algorithm polynomial-time algorithms logarithmic barrier function path following 

Copyright information

© The Mathematical Programming Society, Inc. 1989

Authors and Affiliations

  • Renato D. C. Monteiro
    • 1
  • Ilan Adler
    • 1
  1. 1.Department of Industrial Engineering and Operations ResearchUniversity of CaliforniaBerkeleyUSA

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