A local-minimization-free zero-gradient-sum algorithm for distributed optimization

Abstract

The classical zero-gradient-sum (ZGS) algorithms for distributed optimization require restrictions on the initial conditions or minimization of local cost functions. This paper proposes a sliding mode-based ZGS algorithm that is free of both initial condition restriction and local minimization. Specifically, a sliding manifold is involved to ensure that the sum of local gradients goes to zero within a fixed time under any initial value. Then, a distributed protocol based on the sliding mode is presented to achieve global optimal consensus in a fixed time. The result is also extended to obtain algorithms for accelerated optimization and disturbance rejection. The effectiveness of the results is verified by numerical simulations.