Distributed hybrid impulsive algorithm with supervisory resetting for nonlinear optimization problems

Abstract

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.

A trust‐based resilient consensus algorithm for distributed optimization considering node and edge attacks

“…18 Based on the state impulsive dynamical theory, a distributed hybrid impulsive algorithm was proposed to solve the large-scale nonlinear optimization problems with linear convergence rate. 19 Different from it, 19 this paper considers the optimization problems while the network is under attack.…”

“…Furthermore, to deal with the distributed optimization problems hybrid linear constraints, a discrete‐time algorithm based on matrix and graph theories was developed, and the effectiveness was verified by numerical examples 18 . Based on the state impulsive dynamical theory, a distributed hybrid impulsive algorithm was proposed to solve the large‐scale nonlinear optimization problems with linear convergence rate 19 . Different from it, 19 this paper considers the optimization problems while the network is under attack.…”