An asynchronous Quasi-Newton method for consensus optimization

Mark Eisen, Aryan Mokhtari, Alejandro Ribeiro

Abstract: We introduce the distributed Broyden-Fletcher-Goldfarb-Shanno (D-BFGS) method as an asynchronous decentralized variation of the BFGS quasi-Newton method for solving consensus optimization problems on a penalty function in the primal domain. The D-BFGS method is of interest in problems that are not well conditioned and in which second order information is not readily available, making decentralized first or second order methods ineffective. Convergence of asynchronous D-BFGS is established formally and strong performance advantages relative to other methods are shown numerically.