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

Let A∈ ℝm× nsetminus 0 and P:=x:Ax≤ 0. This paper provides a procedure to compute an upper bound on the following homogeneous Hoffman constant: [ H0(A) := supu∈ ℝn setminus P fracdist(u,P)dist(Au, ℝm_-). ] In sharp contrast to the intractability of computing more general Hoffman constants, the procedure described in this paper is entirely tractable and easily implementable.