# On Robustness in Nonconvex Optimization with Application to Defense Planning

arXiv: https://arxiv.org/abs/2208.09725 · HTML: https://mlsanity.com/paper/2208.09725/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 20 Aug 2022.

## Builds on (most cited first, 7 of 7)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Opportunities and Challenges in Deep Learning Adversarial Robustness: A Survey](https://mlsanity.com/paper/2007.00753/) (2020)
- [Diametrical Risk Minimization: Theory and Computations](https://mlsanity.com/paper/1910.10844/) (2019)
- [Good and Bad Optimization Models: Insights from Rockafellians](https://mlsanity.com/paper/2105.06073/) (2021)
- [Stability analysis for parameterized variational systems with implicit constraints](https://mlsanity.com/paper/1902.07464/) (2019)
- [Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation](https://mlsanity.com/paper/2112.05571/) (2021)

## Abstract (arXiv)

In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed expressions for subgradients and local Lipschitz moduli of min-value functions in nonconvex robust optimization and require only the solution of the nominal problem. The theoretical results are illustrated by examples from military operations research involving mixed-integer optimization models. Across 54 cases examined, the median error in estimating the increase in minimum value is 12%. Therefore, the derived expressions for subgradients and local Lipschitz moduli may accurately inform analysts about the possibility of obtaining cost-effective, parameter-robust decisions in nonconvex optimization.