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arXiv · 2103.12315

Distributionally Robust Optimization with Moment Ambiguity Sets

Jiawang Nie·Liu Yang·Suhan Zhong·Guangming Zhou
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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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Jiawang Nie, Liu Yang, Suhan Zhong, Guangming Zhou. 2021-03-23. Distributionally Robust Optimization with Moment Ambiguity Sets. https://arxiv.org/abs/2103.12315

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