Variable projection methods for large convex quadratic programming

We propose two projection-type methods for solving large quadratic programs. The main feature of these iterative schemes consists in using, at each iteration, a variable projection parameter instead of a fixed one as in the classical projection methods. The convergence may be obtained without restrictive conditions on the projection parameters by using appropriate correction rules that imply, at each iteration, a sufficient decrease in the objective function. The first method uses a correction rule on the descent direction produced by the projection step, while in the second method, the correction formula works adaptively on the value of the variable projection parameter. We give convergence results for the general case of inexact solution of the inner subproblems. The numerical behaviour of the methods is strictly dependent on the sequence of the projection parameters. We introduce a practical nonexpensive updating rule for these parameters and evaluate its effectiveness on large scale test problems.