Quadratic maximization and semidefinite relaxation

In this paper we study a class of quadratic maximization problems and their semidefinite programming (SDP) relaxation, For a special subclass: of dir problems we show that the SDP relaxation provides an exact optimal solution, Another subclass, which is NP-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 uf Goemans and Williamson fur the maximum-cut problem. Finally, we discuss extensions of these results in the presence of a certain type of sign restrictions.