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An improved version of Chubanovís method for solving a homogeneous feasibility problem

Kees Roos(c.roos***at***tudelft.nl)

Abstract: We deal with a recently proposed method of Chubanov [1] for solving linear homogeneous systems with positive variables. Some improvements of Chubanovís method and its analysis are presented. We propose a new and simple cut criterion and show that the cuts defined by the new criterion are at least as sharp as in [1]. The new cut criterion reduces the iteration bound for his Basic Procedure by a factor 5, without changing the order of its strongly polynomial complexity. Our Modified Main Algorithm is in essence the same as Chubanovís Main Algorithm, except that it uses our Modified Basic Procedure as a subroutine. It is shown that it has O(n4L) time complexity, just as in [1]. Some promising computational results are presented, in comparison with the optimization package Gurobi.

Keywords: linear homogeneous systems, algorithm, polynomial-time

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )


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Entry Submitted: 11/29/2016
Entry Accepted: 11/29/2016
Entry Last Modified: 11/29/2016

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