| Issue |
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|
|
|---|---|---|
| Article Number | 71 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2021065 | |
| Published online | 06 July 2021 | |
Second order necessary conditions for optimal control problems of evolution equations involving final point equality constraints
1
CNRS, IMJ-PRG, UMR 7586, Sorbonne Université, case 247, 4 place Jussieu,
75252
Paris, France.
2
School of Mathematics, Sichuan University,
Chengdu,
610064, PR China.
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
9
October
2020
Accepted:
12
June
2021
Abstract
We establish some second order necessary conditions for optimal control problems of evolution equations involving final point equality and inequality constraints. Compared with the existing works, the main difference is due to the presence of end-point equality constraints. With such constraints, we cannot simply use the variational techniques since perturbations of a given control may be no longer admissible. We also cannot use the Ekeland’s variational principle, which is a first order variational principle, to obtain second order necessary conditions. Instead, we combine some inverse mapping theorems on metric spaces and second order linearization of data to obtain our results.
Mathematics Subject Classification: 49K20
Key words: Optimal control / time evolution partial differential equation / second order necessary condition / local minimizer
The research of this author is partially supported by the AFOSR grant FA 9550-18-1-0254 and the CNRS-NSFC PRC Project under grant 271392. She also benefited from the support of the FJMH Program PGMO and from the support to this program from EDF-THALES-ORANGE-CRITEO.
The research of this author is supported by the NSF of China under grants 11971334, 12025105 and 11931011, by the Chang Jiang Scholars Program from the Chinese Education Ministry, and the CNRS-NSFC PRC Project under grant 11530142.
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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