Abstract
We present a new method for solving multivalued variational inequalities, where the underlying function is upper semicontinuous and satisfies a certain generalized monotone assumption. First, we construct an appropriate hyperplane which separates the current iterative point from the solution set. Then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the halfspace containing the solution set. We also analyze the global convergence of the algorithm under minimal assumptions.
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Anh, P.N., Kuno, T. (2012). A Cutting Hyperplane Method for Generalized Monotone Nonlipschitzian Multivalued Variational Inequalities. In: Bock, H., Hoang, X., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25707-0_1
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DOI: https://doi.org/10.1007/978-3-642-25707-0_1
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Online ISBN: 978-3-642-25707-0
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