Uncertainty Partitioning with Probabilistic Feasibility and Performance Guarantees for Chance-Constrained Optimization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908381331062784 |
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| author | Cordiano, Francesco Jafarian, Matin De Schutter, Bart |
| author_facet | Cordiano, Francesco Jafarian, Matin De Schutter, Bart |
| contents | We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists of partitioning the uncertainty domain in a user-defined number of sets, enabling more flexibility in the trade-off between conservatism and computational complexity. We provide sufficient conditions to ensure that our approximated problem is feasible for the original stochastic program, in terms of chance constraint satisfaction. In addition, we perform a rigorous performance analysis, by quantifying the distance between the optimal values of the original and the approximated problem. We show that our approach is tractable for optimization problems that include model predictive control of piecewise affine systems, and we demonstrate the benefits of our approach, in terms of the trade-off between conservatism and computational complexity, on a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20927 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty Partitioning with Probabilistic Feasibility and Performance Guarantees for Chance-Constrained Optimization Cordiano, Francesco Jafarian, Matin De Schutter, Bart Optimization and Control Systems and Control We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists of partitioning the uncertainty domain in a user-defined number of sets, enabling more flexibility in the trade-off between conservatism and computational complexity. We provide sufficient conditions to ensure that our approximated problem is feasible for the original stochastic program, in terms of chance constraint satisfaction. In addition, we perform a rigorous performance analysis, by quantifying the distance between the optimal values of the original and the approximated problem. We show that our approach is tractable for optimization problems that include model predictive control of piecewise affine systems, and we demonstrate the benefits of our approach, in terms of the trade-off between conservatism and computational complexity, on a numerical example. |
| title | Uncertainty Partitioning with Probabilistic Feasibility and Performance Guarantees for Chance-Constrained Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.20927 |