Duality bound method for the general quadratic programming problem with quadratic constraints

The purpose of this article is to develop a branch-and-bound algorithm usin g duality bounds for the general quadratically-constrained quadratic progra mming problem and having the following properties: (i) duality bounds are c omputed by solving ordinary linear programs; (ii) they are at least as good as the lower bounds obtained by solving relaxed problems, in which each no nconvex function is replaced by its convex envelope; (iii) standard converg ence properties of branch-and-bound algorithms for nonconvex global optimiz ation problems are guaranteed. Numerical results of preliminary computation al experiments for the case of one quadratic constraint are reported.