A projection algorithm for non-monotone variational inequalities
Date
2020
Authors
Burachik, R.S.
Millán, R.D.
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Journal article
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Set-Valued and Variational Analysis, 2020; 28(1):149-166
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Abstract
We introduce a projection-type algorithm for solving the variational inequality problem for point-to-set operators, and establish its convergence properties. Namely, we assume that the operator of the variational inequality is continuous in the point-to-set sense, i.e., inner- and outer-semicontinuous. Under the assumption that the dual solution set is not empty, we prove that our method converges to a solution of the variational inequality. Instead of the monotonicity assumption, we require the non-emptiness of the solution set of the dual formulation of the variational inequality. We provide numerical experiments illustrating the behaviour of our iterates. Moreover, we compare our new method with a recent similar one.
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Link to a related website: http://arxiv.org/pdf/1609.09569, Open Access via Unpaywall
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Copyright 2019 Springer Nature B.V.