Abstract.
In this paper we study a class of quadratic maximization problems and their semidefinite programming (SDP) relaxation. For a special subclass of the problems we show that the SDP relaxation provides an exact optimal solution. Another subclass, which is ??-hard, guarantees that the SDP relaxation yields an approximate solution with a worst-case performance ratio of 0.87856.... This is a generalization of the well-known result of Goemans and Williamson for the maximum-cut problem. Finally, we discuss extensions of these results in the presence of a certain type of sign restrictions.
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Received: September 10, 1998 / Accepted: February 12, 1999¶Published online February 23, 2000
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Zhang, S. Quadratic maximization and semidefinite relaxation. Math. Program. 87, 453–465 (2000). https://doi.org/10.1007/s101070050006
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DOI: https://doi.org/10.1007/s101070050006