# Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation

arXiv: https://arxiv.org/abs/1905.07377 · HTML: https://mlsanity.com/paper/1905.07377/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2019.

## Built on by (most cited first, 6 of 6)

- [Conformal Predictive Programming for Chance Constrained Optimization](https://mlsanity.com/paper/2402.07407/) (2024)
- [On data-driven chance constraint learning for mixed-integer optimization problems](https://mlsanity.com/paper/2207.03844/) (2022)
- [Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency](https://mlsanity.com/paper/2106.12199/) (2021)
- [Gradients and Subgradients of Buffered Failure Probability](https://mlsanity.com/paper/2109.05391/) (2021)
- [Sampling-based Pareto Optimization for Chance-constrained Monotone Submodular Problems](https://mlsanity.com/paper/2404.11907/) (2024)
- [Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression](https://mlsanity.com/paper/2603.19907/) (2026)

## Abstract (arXiv)

We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated via a differentiable sample average approximation. We provide theoretical statistical guarantees of the approximation, and illustrate empirically that the reformulation can be directly used by standard nonlinear optimization solvers in the case of single chance constraints. Furthermore, we propose an Sℓ1QP-type trust-region method to solve instances with joint chance constraints. We demonstrate the performance of the method on several problems, and show that it scales well with the sample size and that the smoothing can be used to counteract the bias in the chance constraint approximation induced by the sample approximation.