# Stability and Error Analysis for Optimization and Generalized Equations

arXiv: https://arxiv.org/abs/1903.08754 · HTML: https://mlsanity.com/paper/1903.08754/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Good and Bad Optimization Models: Insights from Rockafellians](https://mlsanity.com/paper/2105.06073/) (2021)
- [Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs](https://mlsanity.com/paper/2602.12273/) (2026)
- [Consistent Approximations in Composite Optimization](https://mlsanity.com/paper/2201.05250/) (2022)

## Abstract (arXiv)

Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations defined on metric spaces and develop bounds on solution errors using the truncated Hausdorff distance applied to graphs and epigraphs of the underlying set-valued mappings and functions. In the process, we extend the calculus of such distances to cover compositions and other constructions that arise in nonconvex problems. The results are applied to constrained problems with feasible sets that might have empty interiors, solution of KKT systems, and optimality conditions for difference-of-convex functions and composite functions.