Distributionally Robust Optimization with Moment Ambiguity Sets
Abstract
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with equivalent moment conic constraints. Under some general assumptions, we prove the DRO is equivalent to a linear optimization problem with moment and psd polynomial cones. A Moment-SOS relaxation method is proposed to solve it. Its asymptotic and finite convergence are shown under certain assumptions. Numerical examples are presented to show how to solve DRO problems.
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Plenum Press
United States
Publication History
Published: 01 January 2023
Accepted: 07 November 2022
Revision received: 14 October 2022
Received: 31 October 2021
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