# An Inexact Weighted Proximal Trust-Region Method

arXiv: https://arxiv.org/abs/2601.09024 · HTML: https://mlsanity.com/paper/2601.09024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 14 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 2 of 2)

- [Inexact Coordinate Descent: Complexity and Preconditioning](https://mlsanity.com/paper/1304.5530/) (2013)
- [The Inexact Cyclic Block Proximal Gradient Method and Properties of Inexact Proximal Maps](https://mlsanity.com/paper/2201.00896/) (2022)

## Abstract (arXiv)

In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical proximity operator. While many functions satisfy this criterion, e.g., the ℓ1-norm defined on ℓ2, many others are precluded by either the topology or the nature of the nonsmooth term. Using the δ-Fr'echet subdifferential, we extend the definition of the inexact proximity operator and enable its use within the aforementioned trust-region algorithm. Moreover, we augment the analysis for the standard trust-region convergence theory to handle proximity operator inexactness with weighted inner products. We first introduce an algorithm to generate a point in the inexact proximity operator and then apply the algorithm within the trust-region method to solve an optimal control problem constrained by Burgers' equation.