# Gradients and Subgradients of Buffered Failure Probability

arXiv: https://arxiv.org/abs/2109.05391 · HTML: https://mlsanity.com/paper/2109.05391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation](https://mlsanity.com/paper/1905.07377/) (2019)
- [Certifiable Risk-Based Engineering Design Optimization](https://mlsanity.com/paper/2101.05129/) (2021)
- [Subdifferential characterization of probability functions under Gaussian distribution](https://mlsanity.com/paper/1705.10160/) (2017)
- [Data-driven optimization of reliability using buffered failure probability](https://mlsanity.com/paper/2107.11176/) (2021)

## Abstract (arXiv)

Gradients and subgradients are central to optimization and sensitivity analysis of buffered failure probabilities. We furnish a characterization of subgradients based on subdifferential calculus in the case of finite probability distributions and, under additional assumptions, also a gradient expression for general distributions. Several examples illustrate the application of the results, especially in the context of optimality conditions.