TY - JOUR

T1 - An improved version of Chubanov's method for solving a homogeneous feasibility problem

AU - Roos, Kees

PY - 2017/9/19

Y1 - 2017/9/19

N2 - We deal with a recently proposed method of Chubanov [A polynomial projection algorithm for linear feasibility problems. Math. Program. 153 (2015), pp. 687–713] for solving linear homogeneous systems with positive variables. Some improvements of Chubanov's 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 Chubanov's Main Algorithm, except that it uses our Modified Basic Procedure as a subroutine. It is shown that it has (Formula presented.) time complexity, just as in [1]. Some promising computational results are presented, in comparison with the optimization package Gurobi.

AB - We deal with a recently proposed method of Chubanov [A polynomial projection algorithm for linear feasibility problems. Math. Program. 153 (2015), pp. 687–713] for solving linear homogeneous systems with positive variables. Some improvements of Chubanov's 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 Chubanov's Main Algorithm, except that it uses our Modified Basic Procedure as a subroutine. It is shown that it has (Formula presented.) time complexity, just as in [1]. Some promising computational results are presented, in comparison with the optimization package Gurobi.

KW - linear homogeneous systems

KW - algorithm

KW - polynomial-time

UR - http://resolver.tudelft.nl/uuid:395ada91-db6e-4cfb-bf96-ba11dec268b2

UR - http://www.scopus.com/inward/record.url?scp=85029715887&partnerID=8YFLogxK

U2 - 10.1080/10556788.2017.1368509

DO - 10.1080/10556788.2017.1368509

M3 - Article

AN - SCOPUS:85029715887

SP - 26

EP - 44

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

ER -