On interior algorithms for linear programming with no regularity assumptions

Authors:
Kurt M Anstreicher
Affiliations:
Department of Management Sciences, University of Iowa, Iowa City, IA USA
Venue:
Operations Research Letters
Year:
1992

Citing 6
Cited 0

A new polynomial-time algorithm for linear programming

Combinatorica
Theory of linear and integer programming

Theory of linear and integer programming
A relaxed revision of Karmarkar's method

Mathematical Programming: Series A and B
A combined phase I-phase II projective algorithm for linear programming

Mathematical Programming: Series A and B
An OL(n3) potential reduction algorithm for linear programming

Mathematical Programming: Series A and B
Path-following methods for linear programming

SIAM Review

Quantified Score

Hi-index	0.00

Visualization

Abstract

The linear programming algorithm of Karmarkar (1984), and all interior methods subsequently devised, require a regularity assumption that the primal and/or dual problem possess a nonempty interior. In this note we devise a polynomial-time interior algorithm which will directly 'process' and linear program, with no regularity assumptions whatsoever, without the addition of any 'M' terms. Our method is based on the application of a combined phase I-phase II algorithm to a combined primal-dual problem.