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

Let A∈ℝ^m× n∖{0} and P:={x:Ax≤ 0} . This paper provides a procedure to compute an upper bound on the following homogeneous Hoffman constant H_0(A):= sup _u∈ℝ^n ∖ P dist (u,P)/ dist (Au, 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.