Error estimates for a multiobjective optimal control of a pointwise tracking problem

¹ Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Santiago, Chile
² Zukunftskolleg, Konstanz University, Universitätsstraße 10, 78464 Konstanz, Germany
³ Department of Mathematics and Statistics, Konstanz University, Universitätsstraße 10, 78464 Konstanz, Germany

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 May 2025
Accepted: 1 April 2026

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.