In multi-objective optimization, minimizing the worst objective can be preferable to minimizing the average objective, as this ensures improved fairness across objectives. Due to the non-smooth nature of the resultant min-max optimization problem, classical subgradient-based approaches typically exhibit slow convergence. Motivated by primal-dual consensus techniques in multi-agent optimization and learning, we formulate a smooth variant of the min-max problem based on the augmented Lagrangian. The resultant Exact Pareto Optimization via Augmented Lagrangian (EPO-AL) algorithm scales better with the number of objectives than subgradient-based strategies, while exhibiting lower per-iteration complexity than recent smoothing-based counterparts. We establish that every fixed-point of the proposed algorithm is both Pareto and min-max optimal under mild assumptions and demonstrate its effectiveness in numerical simulations.
View on arXiv@article{park2025_2504.02833,
title={ Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization },
author={ Sangwoo Park and Stefan Vlaski and Lajos Hanzo },
journal={arXiv preprint arXiv:2504.02833},
year={ 2025 }
}