We consider a nonconvex quadratic program having a linear objective
function and finitely many quadratic inequalty constraints. We
present implementable variants of the SSDP (Successive Semidefinite
Programming) Relaxation Method and the SSILP (Successive Semi-Infinite
LP) Relaxation Method recently proposed by Kojima and Tun{\c c}el.
Each iteration of the variant of the SSDP Relaxation Method is carried
out by solving a finite number of semidefinite programs, while each
iteration of the SSILP Relaxation Method is carried out by solving a
finite number of linear programs. Given any $\epsilon > 0$, both
variants compute an upper bound of the optimal objective value within
$\epsilon$ in a finite number of iterations.