2025/12/23 by Cortild, Daniel, Marschner, Meggie, Staudigl, Mathias
#90C33 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2512.20772
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.