Tuesday, 16:15 - 16:40 h, Room: MA 141

 

Daniel Kuhn
Polyhedrality in distributionally robust optimization

Coauthors: Melvyn Sim, Wolfram Wiesemann

 

Abstract:
Distributionally robust optimization studies stochastic programs whose uncertain parameters follow a distribution that is itself uncertain. The distribution is only known to belong to an ambiguity set defined in terms of certain statistical or structural properties, and the decision-maker is assumed to hedge against the worst-case distribution within the ambiguity set. Most distributionally robust optimization problems studied to date rely on mean, covariance and support information about the uncertain parameters. These problems can often be reformulated as semidefinite programs, which are computationally tractable in theory but suffer from limited scalability in practice. In this talk we propose new uncertainty models specified in terms of maximum variability bounds with polyhedral integrands, minimum variability bounds with polyhedral integrands and polyhedral confidence sets, respectively. We employ these ambiguity sets in the context of standard and risk-averse stochastic programming as well as chance constrained programming, and we show that the resulting distributionally robust optimization problems admit highly scalable reformulations or approximations as linear programs.

 

Talk 3 of the invited session Tue.3.MA 141
"Advances in stochastic programming" [...]
Cluster 22
"Stochastic optimization" [...]

 

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