Distributionally Robust Optimization with Polynomial Robust Constraints

Jiawang Nie () and Suhan Zhong ()
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Jiawang Nie: University of California San Diego
Suhan Zhong: Texas A&M University

Journal of Global Optimization, 2025, vol. 92, issue 3, No 1, 509-534

Abstract: Abstract This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving linear conic optimization with semidefinite constraints. When the DRO problem is SOS-convex, we show that it is equivalent to the linear conic relaxation and it can be solved by the Moment-SOS algorithm. For nonconvex cases, we also give concrete conditions such that the DRO can be solved globally. Numerical experiments are given to show the efficiency of the method.

Keywords: Distributionally robust optimization; Robust constraints; Polynomial; Moment; Relaxation; 90C23; 90C22; 90C15; 90C17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01504-6

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