A Unified Dual Consensus Approach to Distributed Optimization with Globally-Coupled Constraints

This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the feasible region is possibly unbounded. To address such problems, a unified DUal Consensus Algorithm (DUCA) and its proximal variant (Pro-DUCA) are proposed, which are unified frameworks that approximate the method of multipliers applied to the corresponding dual problem in no need of a closed-form dual objective. With varied parameter settings, DUCA and Pro-DUCA not only extend a collection of existing consensus optimization methods to solve the dual problem that they used to be inapplicable to, but also aid in offering new efficient algorithms to the literature. The proposed unified algorithms are shown to achieve $O(1/k)$ convergence rates in terms of optimality and feasibility, providing new or enhanced convergence results for a number of existing methods. Simulations demonstrate that these algorithms outperform several state-of-the-art alternatives in terms of objective and feasibility errors.