An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming
Abstract
We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the use of inexact value and derivative information, enabling the solution of infinite-dimensional problems governed by, e.g., partial differential equations (PDEs). We prove global convergence of our method and under additional regularity assumptions, demonstrate that the sequence of iterates accumulates at a stationary point of our target problem. We demonstrate our method's efficiency on two PDE-constrained optimization examples, showing that its performance is invariant to the PDE discretization size.
Cite
@article{arxiv.2604.07216,
title = {An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming},
author = {Drew P. Kouri},
journal= {arXiv preprint arXiv:2604.07216},
year = {2026}
}