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The design and complexity analysis of randomized coordinate descent methods, and in particular of variants which update a random subset (sampling) of coordinates in each iteration, depends on the notion of expected separable overapproximation (ESO). This refers to an inequality involving the objective function and the sampling, capturing in a compact way certain smoothness properties of the function in a random subspace spanned by the sampled coordinates. ESO inequalities were previouslydoi:10.1080/10556788.2016.1190361 fatcat:bvueahrt4fa7rox4bf6d5ehdmi