| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 87 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2025074 | |
| Published online | 05 November 2025 | |
Optimality conditions for a class of multi-objective control problems
1
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2
Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
* Corresponding author: liux216@nenu.edu.cn
Received:
24
December
2024
Accepted:
4
September
2025
This paper is devoted to studying a class of infinite-dimensional multi-objective control problems. First, an abstract linear system is driven by a leader control and two follower controls. For each leader control, a pair of follower controls is searched for as a Nash equilibrium of the game problem, while the aim of leader controls is to solve a constrained infinite-dimensional optimization problem. The first-order necessary condition for solutions to this optimization problem is given through a finite codimensionality condition. As applications, some multi-objective control problems for wave equations and quasi-linear parabolic equations are studied, respectively.
Mathematics Subject Classification: 49K20 / 93C25
Key words: Multi-objective control problem / necessary condition / Nash equilibrium / finite codimensionality
© The authors. Published by EDP Sciences, SMAI 2025
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