# On global minimizers of quadratic functions with cubic regularization

arXiv: https://arxiv.org/abs/1711.01303 · HTML: https://mlsanity.com/paper/1711.01303/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2017.

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

- [Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness](https://mlsanity.com/paper/2209.01229/) (2022)

## Abstract (arXiv)

In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the last years. First we show that, given any stationary point that is not a global solution, it is possible to compute, in closed form, a new point with a smaller objective function value. Then, we prove that a global minimizer can be obtained by computing a finite number of stationary points. Finally, we extend these results to the case where stationary conditions are approximately satisfied, discussing some possible algorithmic applications.