Aled Williams, "Finding an Optimal Proximity Bound in a Very Special Scenario," WSEAS Transactions on Mathematics, vol. 21, pp. 600-603, 2022, DOI:10.37394/23206.2022.21.68
Aled Williams. Finding an Optimal Proximity Bound in a Very Special Scenario.
WSEAS Transactions on Mathematics. 2022;21:600-603. 10.37394/23206.2022.21.68
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Finding an Optimal Proximity Bound in a Very Special Scenario
Author:
Abstract: Given $$A ∈ Z^{m×n}$$ and $$b ∈ Z^{m}$$, we provide a sharp upper bound for the $$ℓ∞$$ -distance from any vertex of the polyhedron $$P(A, b) = \lbrace x ∈ R^{n} ≥0 : Ax = b\rbrace$$ to a nearby feasible integral point under a strong assumption regarding the dimensions of the matrix A. It is hoped that this result provides motivation for conducting further research into providing more such upper bounds under certain additional assumptions.
Pages: 600-603 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 21, 2022, Art. #68 DOI: 10.37394/23206.2022.21.68
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