A Distributed Approach for the Nonconvex Resource Allocation Problem Over Unbalanced Directed Networks

Abstract

This article deals with the distributed resource allocation problem with a nonconvex objective function over a weight-unbalanced directed communication network, where a coupled equality constraint and a private convex set are considered. To handle this issue, a distributed consensus-based estimator is introduced to track the coupled constraint within a finite time. Then, based on this estimator, a primal–dual distributed optimization approach is designed, where the local dual variable guarantees the global constraint and cooperatively achieves the optimal centralized dual variable. To ensure the stability of the primal subsystem, based on the penalty-like function method, a convex term is added to the augmented Lagrangian multiplier function such that its Hessian matrix over the primal variable is positive definite. Finally, the developed method’s asymptotical convergence rate is established, and its effectiveness is evaluated via two case simulations.