Improved estimation of duality gap in binary quadratic programming using a weighted distance measure
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 218 (2012)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/eor
Quadratic binary programming; Lagrangian duality gap; Semidefinite relaxation; Weighted distance measure; Cell enumeration and hyperplane arrangement;
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- Helmberg, C., 2002. "Semidefinite programming," European Journal of Operational Research, Elsevier, vol. 137(3), pages 461-482, March.
- Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
- Ferrez, J.-A. & Fukuda, K. & Liebling, Th.M., 2005. "Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm," European Journal of Operational Research, Elsevier, vol. 166(1), pages 35-50, October.
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