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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.17344 |
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| _version_ | 1866918395293728768 |
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| author | Choi, Jaeseok Deo, Anand Lagoa, Constantino Subramanyam, Anirudh |
| author_facet | Choi, Jaeseok Deo, Anand Lagoa, Constantino Subramanyam, Anirudh |
| contents | Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its straightforward implementation and ability to preserve problem structure. However, in the rare-event regime where constraint violations must be kept extremely unlikely, the scenario approach becomes computationally infeasible due to the excessively large sample sizes it demands. We address this limitation with a new yet straightforward decision-scaling method that relies exclusively on original data samples and a single scalar hyperparameter that scales the constraints in a way amenable to standard solvers. Our method leverages large deviation principles under mild nonparametric assumptions satisfied by commonly used distribution families in practice. For a broad class of problems satisfying certain practically verifiable structural assumptions, the method achieves a polynomial reduction in sample size requirements compared to the classical scenario approach, while also guaranteeing asymptotic feasibility in the rare-event regime. Numerical experiments spanning finance and engineering applications show that our decision-scaling method significantly expands the scope of problems that can be solved both efficiently and reliably. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17344 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Decision-Scaled Scenario Approach for Rare Chance-Constrained Optimization Choi, Jaeseok Deo, Anand Lagoa, Constantino Subramanyam, Anirudh Optimization and Control 90C15, 60F10, 65C05 Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its straightforward implementation and ability to preserve problem structure. However, in the rare-event regime where constraint violations must be kept extremely unlikely, the scenario approach becomes computationally infeasible due to the excessively large sample sizes it demands. We address this limitation with a new yet straightforward decision-scaling method that relies exclusively on original data samples and a single scalar hyperparameter that scales the constraints in a way amenable to standard solvers. Our method leverages large deviation principles under mild nonparametric assumptions satisfied by commonly used distribution families in practice. For a broad class of problems satisfying certain practically verifiable structural assumptions, the method achieves a polynomial reduction in sample size requirements compared to the classical scenario approach, while also guaranteeing asymptotic feasibility in the rare-event regime. Numerical experiments spanning finance and engineering applications show that our decision-scaling method significantly expands the scope of problems that can be solved both efficiently and reliably. |
| title | Decision-Scaled Scenario Approach for Rare Chance-Constrained Optimization |
| topic | Optimization and Control 90C15, 60F10, 65C05 |
| url | https://arxiv.org/abs/2603.17344 |