An Implementation of Karmarkar's Algorithm for Linear Programming

Ilan Adler, Narendra Karmarkar, Mauricio G.C. Resende, and Geraldo Veiga

This article originally appeared in Mathematical Programming, vol. 44, pp. 297-335, 1989. An errata correcting the description of the power series algorithm was published in Mathematical Programming, vol. 50, p. 415, 1991. The version presented here incorporates these corrections to the body of the article. In addition, we updated references to some articles published in final form after the publication of this paper.


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 code MINOS 4.0.

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