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A Data-Driven Distributionally Robust Bound on the Expected Optimal Value of Uncertain Mixed 0-1 Linear Programming

Guanglin Xu(guanglin-xu***at***uiowa.edu)
Samuel Burer(samuel-burer***at***uiowa.edu)

Abstract: This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from the observed samples and containing the true distribution with a high statistical guarantee. The problem of interest is to investigate the bound on the expected optimal value over the Wasserstein ambiguity set. Under standard assumptions, we reformulate the problem into a copositive program, which naturally leads to a tractable semidefinite-based approximation. We compare our approach with a moment-based approach from the literature on three applications. Numerical results illustrate the effectiveness of our approach.

Keywords: Distributionally robust optimization; Wasserstein metric; copositive programming; semidefinite programming

Category 1: Robust Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Stochastic Programming


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Entry Submitted: 08/24/2017
Entry Accepted: 08/24/2017
Entry Last Modified: 08/24/2017

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