An adaptive algorithm for bound constrained quadratic minimization

A general algorithm for minimizing a quadratic function with bounds on the variables is presented. The new algorithm can use diierent un-constrained minimization techniques on diierent faces. At every face, the minimization technique can be chosen according to he structure of the Hessian and the dimension of the face. The strategy for leaving the face is based on a simple scheme that exploits the properties of the \chopped gradient" introduced by Friedlander and Mart nez in 1989. This strategy guarantees global convergence even in the presence of dual degeneracy, and nite identiication in the nondegenerate case. A slight modiication of the algorithm satisses, in addition, an identiica-tion property in the case of dual degeneracy. Numerical experiments combining this new strategy with conjugate gradients, gradient with retards and direct solvers are presented.