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A note on distributionally robust optimization under moment uncertainty

Qiang Liu, Jia Wu, Xiantao Xiao and Liwei Zhang

Abstract

We considers a distributionally robust optimization problem when the ambiguity set specifies the support as well as the mean and the covariance matrix of the uncertain parameters. After deriving a general deterministic reformulation for the distributionally robust optimization problem, we obtain tractable optimization reformulations when the support set is the whole space and when it is a convex polyhedral set. A hybrid method of Gurobi and a smoothing Newton conjugate gradient method is suggested to solve the tractable optimization problems and numerical results of the hybrid method for solving an illustrative example are reported.

MSC 2010: 90C30

  1. Funding: The research was supported by the National Natural Science Foundation of China under project No. 91330206 and 11571059.

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Received: 2017-02-08
Revised: 2018-01-19
Accepted: 2018-01-24
Published Online: 2018-02-19
Published in Print: 2018-09-25

© 2018 Walter de Gruyter GmbH, Berlin/Boston