We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.
@article{arxiv.2105.09407,
title = {Trilevel and Multilevel Optimization using Monotone Operator Theory},
author = {Allahkaram Shafiei and Vyacheslav Kungurtsev and Jakub Marecek},
journal= {arXiv preprint arXiv:2105.09407},
year = {2024}
}