Adaptive projected SOR algorithms for nonnegative quadratic programming

The optimal value of the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present a novel adaptive PSOR algorithm that adaptively controls the relaxation parameter using the Wolfe conditions. The method and its variants can be applied to various problems without requiring a specific assumption regarding the matrix defining the objective function, and the cost for updating the parameter is negligible in the whole iteration. Numerical experiments show that the proposed methods often perform comparably to (or sometimes superior to) the PSOR method with a nearly optimal relaxation parameter.