Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization
Abstract
In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is either strictly convex in the primal or strictly concave in the dual variables. In this paper, we show convergence under non-strict convexity when a simple, unilateral augmentation term is added. For this purpose, we establish a novel, non-trivial characterization of the limit set of saddle-flow trajectories that allows us to preclude limit cycles. With our presentation we try to unify several existing problem formulations as a projected dynamical system that allows projection of both the primal and dual variables, thus complementing results available in the recent literature.
Cite
@article{arxiv.2010.09496,
title = {Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization},
author = {Adrian Hauswirth and Lukas Ortmann and Saverio Bolognani and Florian Dörfler},
journal= {arXiv preprint arXiv:2010.09496},
year = {2020}
}