Regularized Primal–Dual Subgradient Method for Distributed Constrained Optimization

TLDR: This paper proposes a consensus-based distributed regularized primal-dual subgradient method for distributed constrained optimization, where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint.

Abstract: In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal–dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an $ {\mathcal {O}} {(} {K}^{ {-1/4}} {)}$ convergence rate for general distributed constrained optimization, where ${K}$ is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.