Exact Spectral-Like Gradient Method for Distributed Optimization

Since the initial proposal in the late 80s, spectral gradient methodsvcontinue to receive signicant attention, especially due to their excellent numerical performance on various large scale applications. However, to date, they have not been suciently explored in the context of distributed optimization. In this paper, we consider unconstrained distributed optimization problems where n nodes constitute an arbitrary connected network and collaboratively minimize the sum of their local convex cost functions. In this setting, building from existing exact distributed gradient methods, we propose a novel exact distributed gradient method wherein nodes' step-sizes are designed according to the novel rules akin to those in spectral gradient methods. We re- fer to the proposed method as Distributed Spectral Gradient method (DSG). The method exhibits R-linear convergence under standard as- sumptions for the nodes' local costs and safeguarding on the algorithm step-sizes. We illustrate the method's performance through simulation
examples.