Optimality of Affine Policies in Multi-stage Robust Optimization

Details Optimality of Affine Policies in Multi-stage Robust Optimization Optimality of Affine Policies in Multi-stage Robust Optimization

2009-04-25

arxiv.org/abs/0904.3986v1

Mathematics of Operations Research, Vol. 35, No. 2, May 2010, pp. 363-394

Mathematics

Optimization and Control

35 pages, 7 figures

Scientific paper

10.1287/moor.1100.0444

In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax (worst-case) objective, and convex state costs plus linear control costs. We develop a new proof methodology, which explores the relationship between the geometrical properties of the feasible set of solutions and the structure of the objective function. Apart from providing an elegant and conceptually simple proof technique, the approach also entails very fast algorithms for the case of piecewise affine state costs, which we explore in connection with a classical inventory management application.

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