Distributed Optimization in Fixed-Time.
Year: 2019
Type: preprint
Abstract: This paper presents a method to solve distributed optimization problem within a fixed time over a time-varying communication topology. Each agent in the network can access its private objective function, while exchange of local information is permitted between the neighbors. This study investigates first nonlinear protocol for achieving distributed optimization for time-varying communication topology within a fixed time independent of the initial conditions. For the case when the global objective function is strictly convex, a second-order Hessian based approach is developed for achieving fixed-time convergence. In the special case of strongly convex global objective function, it is shown that the requirement to transmit Hessians can be relaxed and an equivalent first-order method is developed for achieving fixed-time convergence to global optimum. Results are further extended to the case where the underlying team objective function, possibly non-convex, satisfies only the Polyak-Łojasiewicz (PL) inequality, which is a relaxation of strong convexity.
Source: arXiv (Cornell University)
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2944831170