Error estimates for a multiobjective optimal control of a pointwise tracking problem
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910955389059072 |
|---|---|
| author | Fuica, Francisco Volkwein, Stefan |
| author_facet | Fuica, Francisco Volkwein, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error estimates for a multiobjective optimal control of a pointwise tracking problem Fuica, Francisco Volkwein, Stefan Optimization and Control Numerical Analysis 49M25, 58E17, 65N15, 65N30, 90C29 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. |
| title | Error estimates for a multiobjective optimal control of a pointwise tracking problem |
| topic | Optimization and Control Numerical Analysis 49M25, 58E17, 65N15, 65N30, 90C29 |
| url | https://arxiv.org/abs/2505.13743 |