# Sufficient Conditions for Error Distance Reduction in the (ℓ2)-norm Trust Region between Minimizers of Local Nonconvex Multivariate Quadratic Approximates

arXiv: https://arxiv.org/abs/2310.08603 · HTML: https://mlsanity.com/paper/2310.08603/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2023.

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

- [Objective Value Change and Shape-Based Accelerated Optimization for the Neural Network Approximation](https://mlsanity.com/paper/2508.20290/) (2025)

## Abstract (arXiv)

This paper analyzes the sufficient conditions for distance reduction between minimizers of local nonconvex quadratic approximate functions with diagonal Hessian in the (ℓ2)-norm trust regions after two iterations. Some examples illustrate the theoretical results of this study.