A Distributed Algorithm for Nonsmooth Resource Allocation Problems with Directed Networks

This paper studies a nonsmooth convex resource allocation problem subjects to local inequality constrains and global equality constraints. A distributed continuous-time algorithm is designed to solve the problem where each agent only knows the local non-smooth objective function and linear or nonlinear local constraints over a weight-balanced directed network. Through nonsmooth analysis and set-valued LaSalle invariance principle, the global convergence to the optimal solution is analyzed. Meanwhile, the distributed algorithm can converge to the optimal solution from any initial condition. To demonstrate the effectiveness of the proposed distributed algorithm, a numerical example is presented to demonstrate the effectiveness of the distributed algorithm.