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A strongly polynomial-time algorithm for the strict homogeneous linear-inequality feasibility problem

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  • Paulo Oliveira

Abstract

A strongly polynomial-time algorithm is proposed for the strict homogeneous linear-inequality feasibility problem in the positive orthant, that is, to obtain $$x\in \mathbb {R}^n$$ x ∈ R n , such that $$Ax > 0$$ A x > 0 , $$x> 0$$ x > 0 , for an $$m\times n$$ m × n matrix $$A$$ A , $$m\ge n$$ m ≥ n . This algorithm requires $$O(p)$$ O ( p ) iterations and $$O(m^2(n+p))$$ O ( m 2 ( n + p ) ) arithmetical operations to ensure that the distance between the solution and the iteration is $$10^{-p}$$ 10 - p . No matrix inversion is needed. An extension to the non-homogeneous linear feasibility problem is presented. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Paulo Oliveira, 2014. "A strongly polynomial-time algorithm for the strict homogeneous linear-inequality feasibility problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 267-284, December.
    • Handle: RePEc:spr:mathme:v:80:y:2014:i:3:p:267-284
    DOI: 10.1007/s00186-014-0480-y
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    References listed on IDEAS

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    1. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
    2. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
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