Online convex optimization with ramp constraints

Abstract

We study a novel variation of online convex optimization where the algorithm is subject to ramp constraints limiting the distance between consecutive actions. Our contribution is results providing asymptotically tight bounds on the worst-case performance, as measured by the competitive difference, of a variant of Model Predictive Control termed Averaging Fixed Horizon Control (AFHC). Additionally, we prove that AFHC achieves the asymptotically optimal achievable competitive difference within a general class of "forward looking" online algorithms. Furthermore, we illustrate that the performance of AFHC in practice is often much better than indicated by the (worst-case) competitive difference using a case study in the context of the economic dispatch problem.

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