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Since the initial proposal in the late 80s, spectral gradient methodscontinue to receive significant attention, especially due to their excellentnumerical performance on various large scale applications. However, to date,they have not been sufficiently explored in the context of distributedoptimization. In this paper, we consider unconstrained distributed optimizationproblems where $n$ nodes constitute an arbitrary connected network andcollaboratively minimize the sum of their local convex cost functions. In thissetting, building from existing exact distributed gradient methods, we proposea novel exact distributed gradient method wherein nodes' step-sizes aredesigned according to the novel rules akin to those in spectral gradientmethods. We refer to the proposed method as Distributed Spectral Gradientmethod (DSG).  The method exhibits R-linear convergence under standard assumptions for thenodes' local costs and safeguarding on the algorithm step-sizes. We illustratethe method's performance through simulation examples.

Exact Spectral-Like Gradient Method for Distributed Optimization