A path-following inexact Newton method for PDE-constrained optimal control in BV

D. Hafemeyer, F. Mannel*

*Corresponding author for this work


We study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm of the control in the objective. We apply a path-following inexact Newton method to the problems that arise from smoothing the TV seminorm and adding an H1 regularization. We prove in an infinite-dimensional setting that, first, the solutions of these auxiliary problems converge to the solution of the original problem and, second, that an inexact Newton method enjoys fast local convergence when applied to a reformulation of the auxiliary optimality systems in which the control appears as implicit function of the adjoint state. We show convergence of a Finite Element approximation, provide a globalized preconditioned inexact Newton method as solver for the discretized auxiliary problems, and embed it into an inexact path-following scheme. We construct a two-dimensional test problem with fully explicit solution and present numerical results to illustrate the accuracy and robustness of the approach.

Original languageEnglish
Article number3
JournalComputational Optimization and Applications
Issue number3
Pages (from-to)753-794
Number of pages42
Publication statusPublished - 07.2022


Dive into the research topics of 'A path-following inexact Newton method for PDE-constrained optimal control in BV'. Together they form a unique fingerprint.

Cite this