4 research outputs found
Distributed Augmented Lagrangian Method for Link-Based Resource Sharing Problems of Multi-Agent Systems
A multi-agent optimization problem motivated by the management of energy
systems is discussed. The associated cost function is separable and convex
although not necessarily strongly convex and there exist edge-based coupling
equality constraints. In this regard, we propose a distributed algorithm based
on solving the dual of the augmented problem. Furthermore, we consider that the
communication network might be time-varying and the algorithm might be carried
out asynchronously. The time-varying nature and the asynchronicity are modeled
as random processes. Then, we show the convergence and the convergence rate of
the proposed algorithm under the aforementioned conditions.Comment: 9 page
Fast convergence of primal-dual dynamics and algorithms with time scaling for linear equality constrained convex optimization problems
We propose a primal-dual dynamic with time scaling for a linear equality
constrained convex optimization problem, which consists of a second-order ODE
for the primal variable and a first-order ODE for the dual variable. Without
assuming strong convexity, we prove its fast convergence property and show that
the obtained fast convergence property is preserved under a small perturbation.
We also develop an inexact primal-dual algorithm derived by a time
discretization, and derive the fast convergence property matching that of the
underlying dynamic. Finally, we give numerical experiments to illustrate the
validity of the proposed algorithm