An easily computable upper bound on the Hoffman constant for homogeneous inequality systems

Javier Peña

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arXiv · 2302.02193

An easily computable upper bound on the Hoffman constant for homogeneous inequality systems

Javier Peña

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Abstract

Let $A\in \mathbb{R}^{m\times n}\setminus \{0\}$ and $P:=\{x:Ax\le 0\}$. This paper provides a procedure to compute an upper bound on the following homogeneous Hoffman constant: \[ H_0(A) := \sup_{u\in \mathbb{R}^n \setminus P} \frac{\text{dist}(u,P)}{\text{dist}(Au, \mathbb{R}^m_-)}. \] In sharp contrast to the intractability of computing more general Hoffman constants, the procedure described in this paper is entirely tractable and easily implementable.

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Javier Peña. 2023-02-04. An easily computable upper bound on the Hoffman constant for homogeneous inequality systems. https://arxiv.org/abs/2302.02193

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