# Convergence of Successive Linear Programming Algorithms for Noisy Functions

arXiv: https://arxiv.org/abs/2302.07205 · HTML: https://mlsanity.com/paper/2302.07205/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2023.

## Built on by (most cited first, 2 of 2)

- [A Trust-Region Algorithm for Noisy Equality Constrained Optimization](https://mlsanity.com/paper/2411.02665/) (2024)
- [AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning](https://mlsanity.com/paper/2507.04553/) (2025)

## Abstract (arXiv)

Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function and derivative information may be corrupted by noise, however. Sun and Nocedal have recently proposed a remedy for smooth unconstrained problems by means of a stabilization of the acceptance criterion for computed iterates, which leads to convergence of the iterates of a trust-region method to a region of criticality, Sun and Nocedal (2022). We extend their analysis to the successive linear programming algorithm, Byrd et al. (2023a,2023b), for unconstrained optimization problems with objectives that can be characterized as the composition of a polyhedral function with a smooth function, where the latter and its gradient may be corrupted by noise. This gives the flexibility to cover, for example, (sub)problems arising image reconstruction or constrained optimization algorithms. We provide computational examples that illustrate the findings and point to possible strategies for practical determination of the stabilization parameter that balances the size of the critical region with a relaxation of the acceptance criterion (or descent property) of the algorithm.