On Chubanov's method for Linear Programming
Amitabh Basu, Jesus De Loera, Mark Junod
TL;DR
This paper analyzes Chubanov's method for linear programming, providing new proofs and interpretations, and develops strongly polynomial algorithms for specific problem classes, offering alternative proofs for classical results.
Contribution
It introduces concise proofs and interpretations of Chubanov's method and develops strongly polynomial algorithms for special linear feasibility problems.
Findings
New concise proofs of Chubanov's results
Strongly polynomial algorithms for certain classes
Alternative proofs of classical results by Tardos and Vavasis & Ye
Abstract
We discuss the method recently proposed by S. Chubanov for the linear feasibility problem. We present new, concise proofs and interpretations of some of his results. We then show how our proofs can be used to find strongly polynomial time algorithms for special classes of linear feasibility problems. Under certain conditions, these results provide new proofs of classical results obtained by Tardos, and Vavasis and Ye.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Complexity and Algorithms in Graphs · Matrix Theory and Algorithms