No-gap second-order optimality conditions for optimal control of a non-smooth quasilinear elliptic equation
This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is finitely PC2 (continuous and C2 apart from finitely many points). We prove that the control-to-state operator is continuously differentiable...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Bài trích |
| Language: | eng |
| Published: |
ESAIM: COCV 27
2021
|
| Subjects: | |
| Online Access: | https://www.esaim-cocv.org/articles/cocv/abs/2021/02/cocv200066/cocv200066.html https://dlib.phenikaa-uni.edu.vn/handle/PNK/2823 https://doi.org/10.1051/cocv/2020092 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is finitely PC2 (continuous and C2 apart from finitely many points). We prove that the control-to-state operator is continuously differentiable even though the nonlinear coefficient is non-smooth. This enables us to establish “no-gap” second-order necessary and sufficient optimality conditions in terms of an abstract curvature functional, i.e., for which the sufficient condition only differs from the necessary one in the fact that the inequality is strict. A condition that is equivalent to the second-order sufficient optimality condition and could be useful for error estimates in, e.g., finite element discretizations is also provided. |
|---|