A projection algorithm for non-monotone variational inequalities
Optimization and Control
2017-11-29 v2
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.
Cite
@article{arxiv.1609.09569,
title = {A projection algorithm for non-monotone variational inequalities},
author = {Regina S. Burachik and R. Díaz Millán},
journal= {arXiv preprint arXiv:1609.09569},
year = {2017}
}