Year: 2024
Type: article
Abstract: In this paper, we introduce an inexact regularized proximal Newton method (IRPNM) that does not require any line search. The method is designed to minimize the sum of a twice continuously differentiable function f and a convex (possibly non-smooth and extended-valued) function $$\varphi $$ φ . Instead of controlling a step size by a line search procedure, we update the regularization parameter in a suitable way, based on the success of the previous iteration. The global convergence of the sequence of iterations and its superlinear convergence rate under a local Hölderian error bound assumption are shown. Notably, these convergence results are obtained without requiring a global Lipschitz property for $$ \nabla f $$ ∇ f , which, to the best of the authors’ knowledge, is a novel contribution for proximal Newton methods. To highlight the efficiency of our approach, we provide numerical comparisons with an IRPNM using a line search globalization and a modern FISTA-type method.
Authors: Simeon vom Dahl, Christian Kanzow
Institution: University of Würzburg
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4401633541