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...
Lưu vào:
| Tác giả chính: | , , |
|---|---|
| Định dạng: | Bài trích |
| Ngôn ngữ: | eng |
| Nhà xuất bản: |
ESAIM: COCV 27
2021
|
| Chủ đề: | |
| Truy cập trực tuyến: | 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 |
| Từ khóa: |
Thêm từ khóa
Không có từ khóa, Hãy là người đầu tiên đánh dấu biểu ghi này!
|
| Tóm tắt: | 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. |
|---|