  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.
