Continuous-Time Algorithm For Distributed Constrained Optimization Over Directed Graphs

Abstract

This paper presents a distributed continuous-time algorithm to solve the convex optimization problem with local inequality constraints and a globally coupled equality constraint. Unlike the existing related results only considering quadratic or nonquadratic but smooth local objective function, this work takes into account a wider class of objective functions which could be nonquadratic and nonsmooth. Moreover, the communication graphs considered in this paper are weight-balanced digraphs other than the undirected graphs required in most existing results. Although the symmetry property of graphs is no longer satisfied, the proposed algorithm still converges to the optimal solution of the optimization problem. Finally, the efficacy of the proposed algorithm is verified by both theoretical analysis and simulation results.