On the finite convergence of successive SDP relaxation methods

Let F be a subset of the n-dimensional Euclidean spaceR represented in terms of a compact convex subset C0 and a set PF of nitely or in nitely many quadratic functions on R such that F = fx 2 C0 : p(x) 0 (8p( ) 2 PF )g. In this paper, we investigate some fundamental properties related to the nite convergence of the successive SDP (semide nite programming) relaxation method proposed by the authors for approximating the convex hull of F .