A Generalized Continuous-Time Algorithm for Nonsmooth Distributed Convex Optimization

This paper proposes a generalized continuous-time algorithm with a novel auxiliary function to solve a nonsmooth distributed constraint optimization over undirected network. By virtue of the property of auxiliary function, the state solution of continuous-time algorithm is proven to enter the sets of equality and inequality constraints in finite time and stay there forever. Moreover, we demonstrate that the proposed algorithm reaches consensus and finally converges to the optimal solution under several mild assumptions. In contrast to the existing algorithms, the proposed algorithm has the simple structure with fewer state variables. Finally, the simulation results and an application in power system are given to show the efficacy and practicability of the presented algorithm.