A Second-Order Primal–Dual Dynamics for Set Constrained Distributed Optimization Problems

The dynamical system with a second-order + first-order structure has been proven to be effective for solving convex optimization problems with equality constraints. In this brief, this structure is extended to distributed optimization to deal with set-constrained convex optimization problems under strongly connected and weight-balanced directed topology, and a continuous optimization dynamics based on projection operator and primal-dual method is proposed. When proper values of the system parameters are selected, the dynamics converges quickly to the optimal solution of the problem. Finally, two numerical experiments are given to verify the effectiveness of the proposed model.