# A Trust-Region Algorithm for Noisy Equality Constrained Optimization

arXiv: https://arxiv.org/abs/2411.02665 · HTML: https://mlsanity.com/paper/2411.02665/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 12 of 12)

- [Stochastic Optimization Using a Trust-Region Method and Random Models](https://mlsanity.com/paper/1504.04231/) (2015)
- [A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians](https://mlsanity.com/paper/2106.13015/) (2021)
- [Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems](https://mlsanity.com/paper/2211.15943/) (2022)
- [A Fully Stochastic Second-Order Trust Region Method](https://mlsanity.com/paper/1911.06920/) (2019)
- [First- and Second-Order High Probability Complexity Bounds for Trust-Region Methods with Noisy Oracles](https://mlsanity.com/paper/2205.03667/) (2022)
- [A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization](https://mlsanity.com/paper/2301.00477/) (2023)
- [Constrained Optimization in the Presence of Noise](https://mlsanity.com/paper/2110.04355/) (2021)
- [The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case](https://mlsanity.com/paper/2104.02519/) (2021)
- [Convergence of Successive Linear Programming Algorithms for Noisy Functions](https://mlsanity.com/paper/2302.07205/) (2023)
- [An adaptive regularization algorithm for unconstrained optimization with inexact function and derivatives values](https://mlsanity.com/paper/2111.14098/) (2021)
- [Stochastic Ratios Tracking Algorithm for Large Scale Machine Learning Problems](https://mlsanity.com/paper/2305.09978/) (2023)
- [A non-monotone trust-region method with noisy oracles and additional sampling](https://mlsanity.com/paper/2307.10038/) (2023)

## Built on by (most cited first, 1 of 1)

- [High Probability Complexity Bounds of Trust-Region Stochastic Sequential Quadratic Programming with Heavy-Tailed Noise](https://mlsanity.com/paper/2503.19091/) (2025)

## Abstract (arXiv)

This paper introduces a modified Byrd-Omojokun (BO) trust region algorithm to address the challenges posed by noisy function and gradient evaluations. The original BO method was designed to solve equality constrained problems and it forms the backbone of some interior point methods for general large-scale constrained optimization. A key strength of the BO method is its robustness in handling problems with rank-deficient constraint Jacobians. The algorithm proposed in this paper introduces a new criterion for accepting a step and for updating the trust region that makes use of an estimate in the noise in the problem. The analysis presented here gives conditions under which the iterates converge to regions of stationary points of the problem, determined by the level of noise. This analysis is more complex than for line search methods because the trust region carries (noisy) information from previous iterates. Numerical tests illustrate the practical performance of the algorithm.