A sharp regularization error estimate for bang-bang solutions for an iterative Bregman regularization method for optimal control problems

TL;DR

This paper provides a sharp regularization error estimate for bang-bang solutions in an iterative Bregman regularization method applied to optimal control problems, supported by numerical results.

Contribution

It introduces a new sharp a-priori error estimate for bang-bang solutions in Bregman regularization methods for optimal control problems.

Findings

The error estimate is sharp in bang-bang cases.

Numerical examples confirm the theoretical convergence results.

The method effectively handles inequality constraints in optimal control.

Abstract

In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and a regularity condition on the active sets convergence results are presented. Furthermore we show by numerical examples that the provided a-priori estimate is sharp in the bang-bang case.