Error estimates for a multiobjective optimal control of a pointwise tracking problem
Optimization and Control
2025-05-21 v1 Numerical Analysis
Numerical Analysis
Abstract
We analyze a pointwise tracking multiobjective optimal control problem subject to the Poisson problem and bilateral control constraints. To approximate Pareto optimal points and the Pareto front numerically, we consider two different finite element-based scalarization techniques, namely the weighted-sum method and the reference point method, where in both methods many scalar-constrained optimization problems have to be solved. We prove a priori error estimates for both scalarizations. The underlying subproblems of either method are solved with a Barzilai-Borwein gradient method. Numerical experiments illustrate the accuracy of the proposed method.
Cite
@article{arxiv.2505.13743,
title = {Error estimates for a multiobjective optimal control of a pointwise tracking problem},
author = {Francisco Fuica and Stefan Volkwein},
journal= {arXiv preprint arXiv:2505.13743},
year = {2025}
}