Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 35, Issue 2, Pages 363-394Publisher
INFORMS
DOI: 10.1287/moor.1100.0444
Keywords
robust optimization; multistage minimax; optimal policies; convex costs; dynamic; programming; inventory management
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In this paper, we prove the optimality of disturbance-affine control policies in the context of one-dimensional, constrained, multistage 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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