Exact Penalty Design for Distributed Projection-Free Optimization with Event-Triggered Communication

This article investigates distributed convex nonsmooth optimization problems with different feasible constraint sets. To address these types of problems, we develop a projection-free algorithm that employs an exact penalty technique, which outperforms existing methods in the same category, such as the renowned Frank-Wolfe algorithm, in handling different feasible constraint sets. The proposed algorithm not only avoids the prohibitive computation involved in projecting subgradients, but also eliminates the projection of variables in the exact penalty function, unlike conventional exact penalty algorithms. Moreover, we employ an event-triggered scheme for the distributed projection-free algorithm to effectively save communication resources. Furthermore, we demonstrate that the proposed algorithm converges to its optimal solution through nonsmooth Lyapunov analysis and the Filippov solution, and we illustrate its effectiveness by two numerical examples.