Journal of Convex Analysis 32 (2025), No. 1, 199--226
Copyright Heldermann Verlag 2025
Splitting Algorithms for Distributionally Robust Optimization
Luis Briceño-Arias
Departamento de Matemática, Universidad Técnica Federico Santa María, Santiago, Chile
luis.briceno@usm.cl
Sergio López-Rivera
Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile
sergio.lopez@dim.uchile.cl
Emilio Vilches
Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile
emilio.vilches@uoh.cl
We propose different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity operator of the supremum function that appears in the optimization problem. The second method solves an equivalent monotone inclusion formulation derived from the first-order optimality conditions, where the resolvents of the monotone operators involved in the inclusion are computable. The proposed methods are applied to solve the Couette inverse problem with uncertainty and the denoising problem with uncertainty. We present numerical results to compare the efficiency of the algorithms.
Keywords: Distributionally robust optimization, supremum function, proximal mapping, splitting algorithms.
MSC: 47H05, 65K05, 90C15, 90C17, 90C25, 90C47.
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