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arXiv · 1609.09569

A projection algorithm for non-monotone variational inequalities

Regina S. Burachik·R. Díaz Millán
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Abstract

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the problem is only assumed to be continuous in the point-to-set sense, i.e., inner- and outer-semicontinuous. Additionally, we assume non-emptiness of the so-called dual solution set. We prove that the whole sequence of iterates converges to a solution of the variational inequality. Moreover, we provide numerical experiments illustrating the behavior of our iterates. Through several examples, we provide a comparison with a recent similar algorithm.

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Regina S. Burachik, R. Díaz Millán. 2016-09-30. A projection algorithm for non-monotone variational inequalities. https://arxiv.org/abs/1609.09569

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