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

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 {\em 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 … Read more

## Solving the n_1 × n_2 × n_3 Points Problem for n_3 < 6

In this paper, we show enhanced upper bounds of the nontrivial n_1 × n_2 × n_3 points problem for every n_1