Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This article applies splitting techniques developed for set-valued maximal monotone operators to monotone affine variational inequalities, including, as a special case, the classical linear complementarity problem.  give a unified presentation of several splitting algorithms for monotone operators, and then apply these results to obtain two classes of algorithms for affine variational inequalities. The second class resembles classical matrix splitting, but has a novel "under-relaxation" step, and converges under more general conditions. In particular, the convergence proofs do not require the affine operator to be symmetric.  specialize our matrix-splitting-like method to discrete-time optimal control problems formulated as extended linear-quadratic programs in the manner advocated by Rockafellar and ts. The result is a highly parallel algorithm, which  implement and test on the Connection Machine CM-5 computer family.
['Jonathan Eckstein', 'Michael C. Ferris']
I am writing a research paper on a idea Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control
[{"from": "human", "value": "I am writing a research paper on a idea Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This article applies splitting techniques developed for set-valued maximal monotone operators to monotone affine variational inequalities, including, as a special case, the classical linear complementarity problem.  give a unified presentation of several splitting algorithms for monotone operators, and then apply these results to obtain two classes of algorithms for affine variational inequalities. The second class resembles classical matrix splitting, but has a novel \"under-relaxation\" step, and converges under more general conditions. In particular, the convergence proofs do not require the affine operator to be symmetric.  specialize our matrix-splitting-like method to discrete-time optimal control problems formulated as extended linear-quadratic programs in the manner advocated by Rockafellar and ts. The result is a highly parallel algorithm, which  implement and test on the Connection Machine CM-5 computer family."}]