English

Projected proximal gradient trust-region algorithm for nonsmooth optimization

Optimization and Control 2025-01-10 v1

Abstract

We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include worst-case complexity bounds in the case of unbounded model Hessian growth, and introduce a new, simple nonsmooth trust-region subproblem solver based on combining several iterations of proximal gradient descent with a single projection into the trust region, which meets the sufficient descent requirements for algorithm convergence and has promising numerical results.

Keywords

Cite

@article{arxiv.2501.04889,
  title  = {Projected proximal gradient trust-region algorithm for nonsmooth optimization},
  author = {Minh N. Dao and Hung M. Phan and Lindon Roberts},
  journal= {arXiv preprint arXiv:2501.04889},
  year   = {2025}
}