Constant Depth Decision Rules for multistage optimization under uncertainty

Vincent Guigues, Anatoli Juditsky and Arkadi Nemirovski

European Journal of Operational Research, 2021, vol. 295, issue 1, 223-232

Abstract: In this paper, we introduce a new class of decision rules, referred to as Constant Depth Decision Rules (CDDRs), for multistage optimization under linear constraints with uncertainty-affected right-hand sides. We consider two uncertainty classes: discrete uncertainties which can take at each stage at most a fixed number d of different values, and polytopic uncertainties which, at each stage, are elements of a convex hull of at most d points. Given the depthμ of the decision rule, the decision at stage t is expressed as the sum of t functions of μ consecutive values of the underlying uncertain parameters. These functions are arbitrary in the case of discrete uncertainties and are poly-affine in the case of polytopic uncertainties. For these uncertainty classes, we show that when the uncertain right-hand sides of the constraints of the multistage problem are of the same additive structure as the decision rules, these constraints can be reformulated as a system of linear inequality constraints where the numbers of variables and constraints is O(1)(n+m)dμN2 with n the maximal dimension of control variables, m the maximal number of inequality constraints at each stage, and N the number of stages.

Keywords: Stochastic programming; Robust optimization; Decision rules; Stochastic Dual Dynamic Programming, (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:295:y:2021:i:1:p:223-232

DOI: 10.1016/j.ejor.2021.02.042

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