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

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DOI: 10.1007/BF01587075

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

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## Abstract

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, where*L* 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