Distributed Algorithm for Nonsmooth Resource Allocation Problems With Nonlinear Constraints and Its Application to Smart Grids

Abstract

In this article, we study nondifferentiable resource allocation problems (RAPs). In our problem, the decisions of agents are subject to coupling inequality constraints, local inequality constraints, and local convex set constraints. In contrast to existing RAPs, the cost functions are nonsmooth and the inequality constraints are nonsmooth and nonlinear in our problem. Based on differential inclusions and projection methods, we exploit a fully distributed subgradient-based resource allocation algorithm to optimally allocate the network resources. With the help of the set-valued LaSalle invariance principle, we prove the global convergence of the algorithm to the optimal resource allocation of our problem. Finally, our method is applied to the economic dispatch problems of smart grids. With our method, the generations of generating units converge to the optimal power generation.