## An Implementation Of Karmarkar's Algorithm For Linear Programming (1986)

Venue: | Mathematical Programming |

Citations: | 57 - 4 self |

### BibTeX

@ARTICLE{Adler86animplementation,

author = {Ilan Adler and Narendra Karmarkar and Mauricio G. C. Resende and Geraldo Veiga},

title = {An Implementation Of Karmarkar's Algorithm For Linear Programming},

journal = {Mathematical Programming},

year = {1986},

volume = {44},

pages = {297--335}

}

### OpenURL

### 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 code MINOS 4.0. 1. INTRODUCTION We describe in this paper a family of interior point power series affine scaling algorithms based on the linear programming algorithm presented by Karmarkar (1984). Two algorithms from this family, corresponding to first and second order pow...