Muhammad Aslam Noor, Muzaffar Akhter, Khalida Inayat Noor, "Forward-backward resolvent splitting methods for general mixed variational inequalities", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 183139, 12 pages, 2003. https://doi.org/10.1155/S0161171203210462
Forward-backward resolvent splitting methods for general mixed variational inequalities
We use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our methods differ from the known three-step forward-backward splitting of Glowinski, Le Tallec, and M. A. Noor for solving various classes of variational inequalities and complementarity problems. Since general mixed variational inequalities include variational inequalities and complementarity problems as special cases, our results continue to hold for these problems.
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