Distributed Algorithm for Constrained Optimization over Weight-Unbalanced Digraphs

This paper addresses distributed optimization problems with compact convex set constraint and nonsmooth objectives over weight-unbalanced directed communication graphs, where the objective function is a sum of local convex functions endowed only by the corresponding agent. The weight unbalance destroys the doubly-stochastic property required by standard consensus algorithms, while the nonsmooth objectives and coupled constraints further complicate distributed computation. To tackle these challenges, we propose a novel continuous-time projection algorithm that achieves finite-time weight balancing and finite-time convergence to the feasible set from any initial values, followed by asymptotic convergence to an optimal solution. Finally, two numerical examples are performed to substantiate the effectiveness, demonstrating its strong adaptability to both weight-balanced and weight-unbalanced graphs compared with existing methods.