A Global Optimality Criterion for Nonconvex Quadratic Programming over a Simplex

In this paper we propose a global optimality criterion for globally minimizing a quadratic form over the standard simplex which in addition provides a sharp lower bound for the optimal value The approach is based on the solution of a semide nite program SDP and a convex quadratic program QP Since there exist fast polynomial time algorithms for solving SDP s and QP s the computational time for checking the global optimality criterion and for computing the lower bound is reasonable Numerical experiments on random test examples up to variables indicate that the optimality criterion veri es a global solution in almost all instances