Efficient proximal subproblem solvers for a nonsmooth trust-region method

Robert J. Baraldi () and Drew P. Kouri ()
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Robert J. Baraldi: Sandia National Laboratories
Drew P. Kouri: Sandia National Laboratories

Computational Optimization and Applications, 2025, vol. 90, issue 1, No 7, 193-226

Abstract: Abstract In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. We compare algorithm performance on examples from data science and PDE-constrained optimization.

Keywords: Nonsmooth optimization; Nonlinear programming; Trust regions; Large-scale optimization; Proximal Newton’s method; 49M15; 49M37; 65K05; 65K10; 90C06; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00628-x

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