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Convergence of a Randomized Newton Method in Nonconvex Optimization
Abstract
We analyze a stochastic Newton optimization scheme for locating the unique global minimizer of a general nonconvex objective function. The method couples a Newton algorithm to additive Gaussian noise with state-dependent variance. In the bounded domain setting, we prove global almost sure convergence. The proof is based on two features of the algorithm: a nondegenerate exploratory property that ensures entrance into a neighborhood of the minimizer after a finite number of steps, and a decaying-noise property that yields contraction with high probability and prevents infinitely many exits from the neighborhood of the minimum.
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BibTeX
@misc{huynh2026convergence,
title = {{Convergence of a Randomized Newton Method in Nonconvex Optimization}},
author = {Edward Huynh and Björn Engquist},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10465},
eprint = {2609.10465},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10465},
}
RIS
TY - UNPB
TI - Convergence of a Randomized Newton Method in Nonconvex Optimization
AU - Edward Huynh
AU - Björn Engquist
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10465
UR - https://arxiv.org/abs/2609.10465
AB - We analyze a stochastic Newton optimization scheme for locating the unique global minimizer of a general nonconvex objective function. The method couples a Newton algorithm to additive Gaussian noise with state-dependent variance. In the bounded domain setting, we prove global almost sure convergence. The proof is based on two features of the algorithm: a nondegenerate exploratory property that ensures entrance into a neighborhood of the minimizer after a finite number of steps, and a decaying-noise property that yields contraction with high probability and prevents infinitely many exits from the neighborhood of the minimum.
ER -