Abstract
We investigate in this paper the duality gap between the binary quadratic optimization problem and its semidefinite programming relaxation. We show that the duality gap can be underestimated by $${\xi_{r+1}\delta^2}$$ , where ? is the distance between {?1, 1} n and certain affine subspace, and ? r+1 is the smallest positive eigenvalue of a perturbed matrix. We also establish the connection between the computation of ? and the cell enumeration of hyperplane arrangement in discrete geometry.
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