Some Heuristics and Test Problems for Nonconvex Quadratic Programming over a Simplex

In this paper we compare two methods for estimating a global minimizer of an inde nite quadratic form over a simplex The rst method is based on the enumeration of local minimizers of a so called control polytope The second method is based on an approximation of the convex envelope using semide nite programming In order to test the algorithms a method for generating random test problems is presented where the optimal solution is known and the number of binding constraints is prescribed Moreover it is investigated if some modi cations of the objective function in uence the performance of the algorithms Numerical experiments are reported