An iterative Bregman regularization method for optimal control problems with inequality constraints

TL;DR

This paper introduces an iterative Bregman regularization approach for solving optimal control problems with inequality constraints, providing convergence analysis and error estimates without requiring the attainability of the desired state.

Contribution

It develops a novel iterative regularization method based on generalized Bregman distances, with convergence proofs under specific conditions and error estimates, extending previous methods.

Findings

Convergence results under source and regularity conditions

Error estimates for the regularization method

Applicability without assuming attainability of the target state

Abstract

We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition and a regularity condition on the active sets. We do not assume attainability of the desired state. Furthermore, a-priori regularization error estimates are obtained.