Title of Paper:A note on distributionally robust optimization under moment uncertainty

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Date of Publication:2018-09-01

Journal:JOURNAL OF NUMERICAL MATHEMATICS

Included Journals:SCIE

Volume:26

Issue:3

Page Number:141-150

ISSN No.:1570-2820

Key Words:distributionally robust optimization; ambiguity set; tractable optimization reformulation; smoothing Newton conjugate gradient method

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.