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Distributionally Robust Optimization with Decision-Dependent Ambiguity Set

Nilay Noyan(nnoyan***at***sabanciuniv.edu)
Gabor Rudolf(grudolf***at***ku.edu.tr)
Miguel Lejeune(mlejeune***at***gwu.edu)

Abstract: We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover's distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest, and provide an overview of various settings leading to tractable formulations. Some of the arising side results are also of independent interest, including mathematical programming expressions for robustified risk measures in a discrete space. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications.

Keywords: stochastic programming; distributionally robust optimization; decision-dependent ambiguity; earth mover's distances; Wasserstein metric; endogenous uncertainty; decision-dependent probabilities; risk-averse; robustified risk; stochastic scheduling; robust scheduling; robust pre-disaster; random link failures; network interdiction

Category 1: Stochastic Programming


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Entry Submitted: 09/19/2018
Entry Accepted: 09/19/2018
Entry Last Modified: 09/19/2018

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