Improved SDP Bounds for Binary Quadratic Programming

Binary quadratic programming; Semi-definite programming; Reverse enumeration; Branch-and-bound

Authors

  • Baiyi Wu School of Finance, Guangdong University of Foreign Studies, Guangzhou 510420, P.R. China
  • Qun Zhang School of Finance, Guangdong University of Foreign Studies, Guangzhou 510420, P.R. China
June 27, 2018

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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.