An Inexact Weighted Proximal Trust-Region Method
Abstract
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 -norm defined on , many others are precluded by either the topology or the nature of the nonsmooth term. Using the -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.
Cite
@article{arxiv.2601.09024,
title = {An Inexact Weighted Proximal Trust-Region Method},
author = {Leandro Farias Maia and Robert Baraldi and Drew P. Kouri},
journal= {arXiv preprint arXiv:2601.09024},
year = {2026}
}