%A Jonathan Eckstein
%A Michael C. Ferris
%T Operator Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control
%D December 1994
%R 94-17
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X This paper applies splitting techniques developed for set-valued maximal
monotone operators to monotone affine variational inequalities, including
the classical linear complementarity problem. We use
established operator splitting theory to derive convergence results for
six algorithms, one of which is a special case of matrix splitting.
The convergence proofs
do not require the affine operator to be symmetric. We specialize one of
these methods to discrete-time optimal control problems formulated as
extended linear-quadratic programs in the manner advocated by Rockafellar
and Wets. The result is a highly parallel algorithm, which we implement
and test on the Connection Machine CM--5 computer family.