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 Moré 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.