Improved SDP Bounds for Binary Quadratic Programming

Abstract

As a classical combinatorial problem, the binary quadratic programming problem has many applications in finance, statistics, production management, etc. The state-of-the-art solution for solving this problem accurately is based on branch-and-bound frameworks, with the low bound support of a semi-definite programming (SDP) relaxation. This paper generalizes the spectral bounds in the literature and proposes a sequence of improved SDP bounds for the binary quadratic programming problem. Our method relies on the closest binary points to an affine space, which can be found by reverse enumeration technique.