An Infeasible Active Set Method with Combinatorial Line Search for Convex Quadratic Problems with Bound Constraints∗

The minimization of a convex quadratic function under bound constraints is a fundamental building block for solving more complicated optimization problems. The active-set method introduced by Bergounioux et al. [1, 2] has turned out to be a powerful, fast and competitive approach for this problem. Hintermüller et al. [15] provide a theoretical explanation of its efficiency by interpreting it as a semismooth Newton method. One major drawback of this method lies in the fact that it is not globally convergent for all classes of convex quadratic objectives. Several modifications were introduced recently, that ensure global convergence. In this paper we introduce yet another modified version of this active set method, which aims at maintaining the combinatorial flavour of the original semismooth Newton method. We prove global convergence for our modified version and show it to be competitive on a variety of difficult classes of test problems.