A DPG method for linear quadratic optimal control problems
Optimization and Control
2023-08-21 v1 Numerical Analysis
Numerical Analysis
Abstract
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it through first order optimality conditions. Furthermore, we systematically develop a priori as well as a posteriori error estimates. Our proposed method can be applied to a wide range of constrained optimal control problems subject to, e.g., scalar second-order PDEs and the Stokes equations. Numerical experiments that illustrate our theoretical findings are presented.
Cite
@article{arxiv.2308.09169,
title = {A DPG method for linear quadratic optimal control problems},
author = {Thomas Führer and Francisco Fuica},
journal= {arXiv preprint arXiv:2308.09169},
year = {2023}
}