Robust Dual Dynamic Programming

Angelos Georghiou · Angelos Tsoukalas · Wolfram Wiesemann

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Risk and Portfolio Optimization Advanced Control Systems Optimization Advanced Optimization Algorithms Research

Abstract

In the paper “Robust Dual Dynamic Programming,” Angelos Georghiou, Angelos Tsoukalas, and Wolfram Wiesemann propose a novel solution scheme for addressing planning problems with long horizons. Such problems can be formulated as multistage robust optimization problems. The proposed method takes advantage of the decomposable nature of these problems by bounding the costs arising in the future stages through lower and upper cost-to-go functions. The proposed scheme does not require a relatively complete recourse, and it offers deterministic upper and lower bounds throughout the execution of the algorithm. The promising performance of the algorithm is shown in a stylized inventory-management problem in which the proposed algorithm achieved the optimal solution in problem instances with 100 time stages in a few minutes.

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References

2010Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems 2013Solving two-stage robust optimization problems using a column-and-constraint generation method 2004Adjustable robust solutions of uncertain linear programs 1997Introduction to Stochastic Programming 2014Distributionally Robust Convex Optimization 2010Distributionally Robust Optimization and Its Tractable Approximations 1985Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs 2010Analysis of stochastic dual dynamic programming method

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