Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Luis Briceño-Arias

Departamento de Matemática, Universidad Técnica Federico Santa María, Santiago, Chile

luis.briceno@usm.cl

Emilio Vilches

Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

emilio.vilches@uoh.cl

Keywords

  • Distributionally robust optimization
  • supremum function
  • proximal mapping
  • splitting algorithms

Mathematics Subject Classification

47H05, 65K05, 90C15, 90C17, 90C25, 90C47

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Suggested citation

L. Briceño-Arias, S. López-Rivera, E. Vilches. “Splitting Algorithms for Distributionally Robust Optimization.” Journal of Convex Analysis 32 (2025), No. 1, 199–226. https://doi.org/10.68381/jca32013

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press.