Distributed hybrid impulsive algorithm with supervisory resetting for nonlinear optimization problems

A distributed impulsive algorithm is presented for solving large-scale nonlinear optimization problems, which is based on state-dependent impulsive dynamical system theory. The optimization problem, whose objective function is a sum of convex and continuously differentiable functions, is solved over a multi-agent network system. The proposed algorithm takes distributed updates in continuous-time part and centralized updates in discrete-time part, which can improve the convergence performance. With stability theory of impulsive dynamical systems, the proposed impulsive algorithm is proved to converge to one optimal solution, and under certain conditions, agents' states are proved to converge at a linear convergence rate. In numerical simulation, compared with conventional distributed continuous-time algorithm, the performance advantage of the proposed impulsive method is demonstrated.