Distributed Nonsmooth Constrained Optimization Algorithm under Weight-unbalanced Directed Graph

This paper studies a class of distributed nonsmooth constrained optimization problem under weight-unbalanced directed communication network, which contains the local set constraints and the global coupled nonlinear inequality constraints. Moreover, the involved functions in the optimization problem are nonsmooth. To tackle the challenges caused by the unbalanced communication network and the nonsmooth functions, a novel distributed projection optimization algorithm, based on Moreau-Yosida approximate function and the distributed estimator, is proposed in this article. The effectiveness of our presented algorithm is verified by stability analysis and numerical simulations.