Limited memory quasi-Newton methods for problems with box constraints

The paper describes new limited memory quasi-Newton algorithms for large scale nonconvex problems with box constraints. The algorithms employ a direction of descent obtained by applying limited memory quasi-Newton updates. In order to cope with box constraints a projection operator on a feasible set is applied. We introduce several algorithms which mainly differ by a directional minimization rule. We show that for the considered line search rules, under the assumption that the objective function is strictly convex, the limited memory BFGS versions are globally convergent. Furthermore, we are able to show that after a finite number of iterations the methods identify an active set at a solution. We believe that the proposed algorithms are competitive to L-BFGS-B algorithm. We give some numerical results which support our claim.