Event-triggered primal-dual design with linear convergence for distributed nonstrongly convex optimization

This paper designs continuous-time algorithms with linear convergence for solving distributed convex optimization problems without a strongly convex condition. The proposed primal-dual algorithms operate under weight-balanced digraphs and the dual variables are not exchanged with neighbors, which makes the algorithm more efficient. To save communication resources, we propose a class of event-triggered communication (ETC) schemes, which includes static and dynamic counterparts with the latter being more effective in communication resource saving. Furthermore, using Lyapunov theory, we prove that the distributed event-triggered algorithms converge to the optimum set with exact linear convergence rates. Finally, we present a comparison example that validates the effectiveness of the proposed algorithms in reducing communication burdens.