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arXiv · 2601.09024

An Inexact Weighted Proximal Trust-Region Method

Leandro Farias Maia·Robert Baraldi·Drew P. Kouri
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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 $\ell_1$-norm defined on $\ell_2$, many others are precluded by either the topology or the nature of the nonsmooth term. Using the $\delta$-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.

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Leandro Farias Maia, Robert Baraldi, Drew P. Kouri. 2026-01-13. An Inexact Weighted Proximal Trust-Region Method. https://arxiv.org/abs/2601.09024

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