# Mixed Newton Method for Optimization in Complex Spaces

arXiv: https://arxiv.org/abs/2407.20367 · HTML: https://mlsanity.com/paper/2407.20367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 1 of 1)

- [Optimization in complex spaces with the Mixed Newton Method](https://mlsanity.com/paper/2207.04265/) (2022)

## Abstract (arXiv)

In this paper, we modify and apply the recently introduced Mixed Newton Method, which is originally designed for minimizing real-valued functions of complex variables, to the minimization of real-valued functions of real variables by extending the functions to complex space. We show that arbitrary regularizations preserve the favorable local convergence properties of the method, and construct a special type of regularization used to prevent convergence to complex minima. We compare several variants of the method applied to training neural networks with real and complex parameters.