New Estimates for Practical Robust Negativity of Multilinear Functions

In this paper, we address a fundamental NP-hard problem which arises in many application areas: Determine whether a multilinear function f(x) is negative for all x in a hypercube X. Consistent with the emerging literature, with the goal being to reduce the computational burden, we consider a relaxation of this robust negativity problem. Specifically, we seek to determine whether f(x) remains negative for all x in X except possibly on a set of "acceptably small" volume.