ON THE MAXIMIZATION OF A CONCAVE QUADRATIC FUNCTION WITH BOX CONSTRAINTS

A new method for maximizing a concave quadratic function with bounds on the variables is introduced. The new algorithm combines conjugate gradients with gradient projection techniques, as the algorithm of More and Toraldo [SIAM J. Optimization, 1 (1991), pp, 93-113] and other well-known methods do. A new strategy for the decision of leaving the current face is introduced that makes it possible to obtain finite convergence even for a singular Hessian and in the presence of dual degeneracy. Numerical experiments are presented.