| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 100 | |
| Number of page(s) | 52 | |
| DOI | https://doi.org/10.1051/cocv/2025075 | |
| Published online | 07 January 2026 | |
Second-order optimality conditions for time-optimal control problems governed by semilinear parabolic equations
1
Department of Mathematics, FPT University, Hoa Lac Hi-Tech Park, Hanoi, Vietnam
2
Department of Optimization and Scientific Computing, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Hanoi, Vietnam
3
Faculty of Mathematics, University of Duisbug-Essen, Thea-Leymann-Strasse 9, 45127 Essen, Germany
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
9
January
2025
Accepted:
9
September
2025
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the locally optimal solution to time-optimal control problems, we derive first- and second-order necessary optimality conditions of KKT-type and second-order sufficient conditions for locally optimal solutions to the problem and establish regularity of Lagrange multipliers.
Mathematics Subject Classification: 49K20 / 35K20
Key words: Time-optimal control / necessary first- and second-order optimality conditions / second-order sufficient condition / semilinear parabolic control / mixed pointwise constraints / final point constraints
© The authors. Published by EDP Sciences, SMAI 2026
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