Abstract

We consider the problem of approximating the global maximum of a quadratic program (QP) with n variables subject to bound constraints. Based on the results of Goemans and Williamson [4] and Nesterov [6], we show that a 4=7 approximate solution can be obtained in polynomial time. Key words. Quadratic programming, global maximizer, approximation algorithm This author is supported in part by NSF grant DMI-9522507. 1 Introduction Consider the quadratic programming (QP) problem ¯ q(Q) := Maximize q(x) := x T Qx (QP) Subject to \Gammae x e; where Q 2 ! n\Thetan is given and e 2 ! n is the vector of all ones. Let ¯ x = ¯ x(Q) be a maximizer of the problem. In this paper, without loss of generality, we assume that ¯ x 6= 0. Normally, there is a linear term in the objective function: q(x) = x T Qx + c T x. However, the problem can be homogenized as Maximize q(x) := x T Qx + tc T x Subject to \Gammae x e; \Gamma1 t 1 by adding a scalar variable t. There always is an opti...

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