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 con-structed according to the distributed continuous time projection algorithm of the strongly connected weighted equi-librium directed graph,the equilibrium solution under this algorithm is proved to be the optimal solution of the dis-tributed optimization problem,as well as the convergence analysis of the algorithm is performed.Finally,the effect-iveness of the algorithm is verified by numerical simulation.
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维普
