Uncertainty Partitioning with Probabilistic Feasibility and Performance Guarantees for Chance-Constrained Optimization

Fuente: arXiv
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Autori principali: Cordiano, Francesco, Jafarian, Matin, De Schutter, Bart
Natura: Preprint
Pubblicazione: 2025
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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