Cone Ordering in Distributionally Robust Optimization with Set-Valued Probabilities

Davide La Torre

doi:10.1007/s10957-026-02992-6

Cone Ordering in Distributionally Robust Optimization with Set-Valued Probabilities

2026-04-29

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DOI：10.1007/s10957-026-02992-6

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We extend the classical distributionally robust optimization framework by introducing set valued probabilities along with an ordering between sets based on convex, pointed cones where we define A <= CB double left right arrow A subset of B-C, with C a closed convex pointed cone. This ordering generalizes inclusion and allows for the modeling of directional preferences and asymmetries. Within this framework, we redefine robustness, convexity, and minimizers; we establish scalarization results, derive optimality conditions, and prove stability theorems. The framework offers a unifying perspective linking robust optimization, set-valued analysis, and cone ordering preferences. An application to the notion of Certainty Equivalent is provided at the end.

Keywords:

Robust Optimization

Set-Valued Probabilities

Set Optimization

Certainty Equivalent

Cone Ordering in Distributionally Robust Optimization with Set-Valued Probabilities

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