| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 24 | |
| Number of page(s) | 27 | |
| DOI | https://doi.org/10.1051/cocv/2021028 | |
| Published online | 26 March 2021 | |
Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations*
1
School of Mathematics and Physics, China University of Geosciences (Wuhan),
Wuhan
430074, P.R. China.
2
Center for Applied Mathematics, Tianjin University,
Tianjin
300072, P.R. China.
** Corresponding author: hanbing272003@aliyun.com
Received:
14
January
2020
Accepted:
10
March
2021
In this paper, we study second-order optimality conditions for some optimal control problems governed by some semi-linear parabolic equations with periodic state constraint in time. We obtain a necessary condition and a sufficient condition in terms of the second order derivative of the associated Lagrangian. These two conditions correspond to the positive definite and the nonnegativity of the second order derivative of the Lagrangian on the same cone, respectively.
Mathematics Subject Classification: 49K20 / 35B10 / 90C48
Key words: Semi-linear parabolic equations / periodic state constraint / second order optimality conditions
© EDP Sciences, SMAI 2021
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