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A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities

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Generalized Convexity, Generalized Monotonicity and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 77))

Abstract

We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, closed, lower hemicontinuous, and bounded on each bounded subset (it is not necessarily continuous). Some numerical test problems are implemented by using MATLAB with encouraging effectiveness.

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Bao, T.Q., Khanh, P.Q. (2005). A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities. In: Eberhard, A., Hadjisavvas, N., Luc, D.T. (eds) Generalized Convexity, Generalized Monotonicity and Applications. Nonconvex Optimization and Its Applications, vol 77. Springer, Boston, MA. https://doi.org/10.1007/0-387-23639-2_6

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