Distributed Optimization with Coupled Constraints over Time-Varying Digraph

TL;DR

This paper introduces a privacy-preserving distributed convex optimization algorithm for time-varying directed networks with coupled constraints, achieving an $O(1/k)$ convergence rate.

Contribution

It develops a novel primal-dual based distributed algorithm that handles nonsmooth objectives and network-wide coupled constraints over time-varying directed graphs.

Findings

Achieves $O(1/k)$ convergence rate in optimality.

Handles nonsmooth local objective functions.

Operates over time-varying directed communication networks.

Abstract

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide coupled. This type of problem arises from many areas, such as economic dispatch, network utility maximization, and demand response. Integrating the decomposition by right hand side allocation and primal-dual methods, the proposed algorithm is able to handle the distributed optimization over networks with time-varying directed graph in fully distributed fashion. This algorithm does not require the communication of sensitive information, such as primal variables, for privacy issues. Further, we show that the proposed algorithm is guaranteed to achieve an $O(1/k)$ rate of convergence in terms of optimality based on duality analysis under the condition that local objective functions are strongly convex but not necessarily differentiable, and the subdifferential of local inequalities is bounded. We simulate the proposed algorithm to demonstrate its remarkable performance.