Risk-averse optimization under distributional uncertainty with Rockafellian relaxation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915933030711296 |
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| author | Antil, Harbir Bustos, Alonso J. Carney, Sean P. Venegas, Benjamín |
| author_facet | Antil, Harbir Bustos, Alonso J. Carney, Sean P. Venegas, Benjamín |
| contents | A framework for risk-averse optimization problems is introduced that is resilient to ambiguities in the true form of the underlying probability distribution. The focus is on problems with partial differential equations (PDEs) as constraints, although the formulation is more broadly applicable. The framework is based on combining risk measures with problem relaxation techniques, and it builds off of previous advances for risk-neutral problems. This work advances the existing theory with strengthened $Γ$-convergence results, novel existence results and first-order optimality criteria. In particular, the theoretical approach naturally accommodates infinite-dimensional probability spaces; no finite-dimensional noise assumption is needed. The framework blends aspects of both distributionally robust optimization (DRO) and distributionally optimistic optimization (DOO) approaches. The DRO aspect facilitates strong out-of-sample performance, while the DOO aspect takes care of adversarial and outlier data, as illustrated with numerical examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00226 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Risk-averse optimization under distributional uncertainty with Rockafellian relaxation Antil, Harbir Bustos, Alonso J. Carney, Sean P. Venegas, Benjamín Optimization and Control 49M37, 90C30, 93C20, 93E20, 49K20, 49J20 A framework for risk-averse optimization problems is introduced that is resilient to ambiguities in the true form of the underlying probability distribution. The focus is on problems with partial differential equations (PDEs) as constraints, although the formulation is more broadly applicable. The framework is based on combining risk measures with problem relaxation techniques, and it builds off of previous advances for risk-neutral problems. This work advances the existing theory with strengthened $Γ$-convergence results, novel existence results and first-order optimality criteria. In particular, the theoretical approach naturally accommodates infinite-dimensional probability spaces; no finite-dimensional noise assumption is needed. The framework blends aspects of both distributionally robust optimization (DRO) and distributionally optimistic optimization (DOO) approaches. The DRO aspect facilitates strong out-of-sample performance, while the DOO aspect takes care of adversarial and outlier data, as illustrated with numerical examples. |
| title | Risk-averse optimization under distributional uncertainty with Rockafellian relaxation |
| topic | Optimization and Control 49M37, 90C30, 93C20, 93E20, 49K20, 49J20 |
| url | https://arxiv.org/abs/2604.00226 |