Error estimates for joint Tikhonov- and Lavrentiev-regularization of constrained control problems

TL;DR

This paper derives error estimates for combined Tikhonov- and Lavrentiev-regularization in constrained control problems, showing conditions under which regularized solutions approximate unconstrained solutions.

Contribution

It provides new error bounds for joint regularization methods and clarifies when regularized solutions preserve unconstrained problem properties.

Findings

Error estimates for Tikhonov regularization error

Regularized solutions match unconstrained solutions under certain conditions

Small regularization parameter ensures no active constraints in solutions

Abstract

We consider joint Tikhonov- and Lavrentiev-regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of this results we show, that if the solution of the unconstrained problem has no active constraints, the same holds for the Tikhonov-regularized solution if the regularization parameter is small enough and a certain source condition is fulfilled.