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arXiv · 2512.20772

Regularization methods for solving hierarchical variational inequalities with complexity guarantees

Daniel Cortild·Meggie Marschner·Mathias Staudigl
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Abstract

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and equilibrium selection problems. In a real Hilbert space setting, we combine a Tikhonov regularization and a proximal penalization to develop a flexible double-loop method for which we prove asymptotic convergence and provide rate statements in terms of gap functions. Our method is flexible, and effectively accommodates a large class of structured operator splitting formulations for which fixed-point encodings are available. Finally, we validate our findings numerically on various examples.

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Daniel Cortild, Meggie Marschner, Mathias Staudigl. 2025-12-23. Regularization methods for solving hierarchical variational inequalities with complexity guarantees. https://arxiv.org/abs/2512.20772

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