On the solution of monotone nested variational inequalities

Lorenzo Lampariello; Gianluca Priori; Simone Sagratella

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arXiv · 2105.13463

On the solution of monotone nested variational inequalities

Lorenzo Lampariello·Gianluca Priori·Simone Sagratella

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Abstract

We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in the literature to guarantee the convergence to solutions of the nested variational inequality. Specifically, we only need monotonicity of the upper- and the lower-level variational inequalities. Also, we provide the first complexity analysis for nested variational inequalities considering optimality of both the upper- and lower-level.

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Lorenzo Lampariello, Gianluca Priori, Simone Sagratella. 2021-05-27. On the solution of monotone nested variational inequalities. https://arxiv.org/abs/2105.13463

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