Robustness certificates in data-driven non-convex optimization with additively-uncertain constraints
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910031691120640 |
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| author | Gallo, Alexander J Zoggia, Massimiliano Falsone, Alessandro Prandini, Maria Garatti, Simone |
| author_facet | Gallo, Alexander J Zoggia, Massimiliano Falsone, Alessandro Prandini, Maria Garatti, Simone |
| contents | We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite data-set, according to the scenario robust optimization paradigm. By exploiting the structure of the constraints, we show that both a priori and a posteriori distribution-free probabilistic robustness certificates for a possibly sub-optimal solution to the resulting data-driven optimization problem can be obtained with minimal computational effort. Building on these results, we also discuss a one-shot and an incremental procedure to determine the size of the data-set so as to guarantee a user-chosen robustness level. Notably, both the a posteriori robustness assessment and incremental data-set sizing do not require to solve the non-convex scenario program. A comparative analysis performed on the unit commitment problem using real data reveals a limited increase in conservativeness with a significant computational saving with respect to the application of scenario theory results for general, non necessarily structured, non-convex problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robustness certificates in data-driven non-convex optimization with additively-uncertain constraints Gallo, Alexander J Zoggia, Massimiliano Falsone, Alessandro Prandini, Maria Garatti, Simone Optimization and Control Systems and Control We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite data-set, according to the scenario robust optimization paradigm. By exploiting the structure of the constraints, we show that both a priori and a posteriori distribution-free probabilistic robustness certificates for a possibly sub-optimal solution to the resulting data-driven optimization problem can be obtained with minimal computational effort. Building on these results, we also discuss a one-shot and an incremental procedure to determine the size of the data-set so as to guarantee a user-chosen robustness level. Notably, both the a posteriori robustness assessment and incremental data-set sizing do not require to solve the non-convex scenario program. A comparative analysis performed on the unit commitment problem using real data reveals a limited increase in conservativeness with a significant computational saving with respect to the application of scenario theory results for general, non necessarily structured, non-convex problems. |
| title | Robustness certificates in data-driven non-convex optimization with additively-uncertain constraints |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2602.21090 |