Convex dynamics: properties of invariant sets

A greedy algorithm for scheduling and digital printing with inputs in a polytope lying in an affine space, and vertices of this polytope as successive outputs, has recently been proven to be bounded for any polytope in any dimension in the case when the norm on errors is the Euclidean norm. This boundedness property follows readily from the existence of some invariant sets (both in the affine space and in the associated vector space), for the dynamics associated to the algorithm. We prove several general properties of such invariant sets under the assumption that the greed of the algorithm is driven by the Euclidean norm.

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