Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

Yong Xia, Ruey-Lin Sheu, Xiaoling Sun and Duan Li

European Journal of Operational Research, 2012, vol. 218, issue 2, 351-357

Abstract: We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.

Keywords: Quadratic binary programming; Lagrangian duality gap; Semidefinite relaxation; Weighted distance measure; Cell enumeration and hyperplane arrangement (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:218:y:2012:i:2:p:351-357

DOI: 10.1016/j.ejor.2011.10.034

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