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Abstract: We consider three parametric relaxations of the 0-1 quadratic programming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maximum eigenvalue of a bordered matrix. When minimized over the parameter, each of the relaxations provides an upper bound on the original discrete problem. Moreover, these bounds are efficiently computable. Our main result is that, surprisingly, all three bounds are equal. This author ... (Update)
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...C # : In general, it may be more advantageous to choose a particular dense row and column for the vector b. Therefore, from Theorem 4. 1 in [13], an equivalent max min problem is the parametric trust region subproblem (TRP ) n 1) max u t e=0 min x t x=n x t (C Gamma...
.... in practice, see e.g. 12, 18, 15] Other theoretical results for general objectives and further relaxed constraints appear in [31, 46] In [38], several unrelated bounds for MC are shown to be equivalent. These bounds include the box relaxation Gammae x e, the trust region...
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BibTeX entry: (Update)
S. POLJAK and H. WOLKOWICZ. Convex relaxations of 0-1 quadratic programming. Technical Report 93-18, DIMACS, 1993. http://citeseer.ist.psu.edu/poljak93convex.html More
@techreport{ poljak93convex,
author = "Svatopluk Poljak and Henry Wolkowicz",
title = "Convex Relaxations of 0-1 Quadratic Programming",
number = "93-18",
year = "1993",
url = "citeseer.ist.psu.edu/poljak93convex.html" }
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