A priori stopping rule for an iterative Bregman method for optimal control problems

TL;DR

This paper develops an a priori stopping rule for an iterative Bregman regularization method applied to constrained optimal control problems, with theoretical error estimates and numerical validation.

Contribution

It introduces a new a priori stopping rule for Bregman-based iterative methods in optimal control, including implementation details and numerical results.

Findings

Noise error estimate for perturbed data

Effective implementation with semi-smooth Newton method

Numerical validation of the stopping rule

Abstract

In this article we continue our investigation of the iterative regularization method for optimization problems based on Bregman distances. The optimization problems are subject to pointwise inequality constraints in $L^2(\Omega)$. We provide an estimate for the noise error for perturbed data, which can be used to construct an a priori stopping rule. Furthermore we show how to implement our method with a semi-smooth Newton method using finite elements and present numerical results for the stopping rule.