Distributed Continuous-time Non-smooth Convex Optimization Analysis With Coupled Constraints Over Directed Graphs

In this paper, we study a class of distributed optimization problems whose objective is to minimize the value of a non-smooth global cost function while satisfying the coupling inequality constraint and the local feasible set constraint. First, we extend the original distributed continuous-time projection algorithm with linear algebraic theory analysis to design an algorithm for strongly connected weighted-balanced directed communication network topology graphs. Second, under the assumption that the local cost function and the coupled inequality constraint function are non-smooth convex functions, we use the Moreau-Yosida function regularization to make the objective function and the constraint function approximately smooth and differentiable. Then, the Lyapunov function is constructed according to the distributed continuous time projection algorithm of the strongly connected weighted equilibrium directed graph, the equilibrium solution under this algorithm is proved to be the optimal solution of the distributed optimization problem, as well as the convergence analysis of the algorithm is performed. Finally, the effectiveness of the algorithm is verified by numerical simulation. © 2024 Science Press. All rights reserved.