Distributed asynchronous non-smooth optimization with coupled equality and bounded constraints

This paper considers a distributed convex optimization problem with a linearly coupled equality constraint and non-smooth objective function, in which heterogeneous time delays exist over the communication network. Based on the passivity of primal–dual dynamics, a distributed asynchronous algorithm that is robust to heterogeneous time delays over the network is proposed. By transforming the output information using the scattering variables and transmitting the scattering variables across the network, convergence to the optimal solution can be guaranteed with a distributed asynchronous method. Moreover, the convergence condition, which is irrelative to the heterogeneous delay parameters, is obtained through Lyapunov analysis. This means the proposed algorithm can achieve convergence to the optimal solution without the heterogeneous delay information. © 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.