Distributed projection gradient algorithm with constraints based on general directed graphs*
Zhengquan Yang, Xiuwei Yang, Zhiyun Gao · 2023
A distributed constrained optimization problem with strongly convex functions is researched in this article. The network structure between the multi agents is weight-unbalanced. Each agent’s state is constrained to a local set and an inequality. A new distributed projected gradient coordination algorithm is given based on the problem, so that the agents can solve the distributed optimization only according to local inequality constraints and local constraint. The new distributed algorithm uses the left eigenvector of the Laplace matrix to eliminate the imbalance of the graph. In this study, no special initialization procedure is required. Using the set-valued Lyapunov stability theory and Lassalle Invariance Principle, it is proved that the proposed system can achieve global consensus under the optimal point. Two numerical simulation examples are given, and show that multi-agents can come to the global optimal point asymptotically. Therefore, the useful of the distributed alaorithm is proven.