On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control
This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus the associated control-to-state operator is, in general, not G...
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| Định dạng: | Bài trích |
| Ngôn ngữ: | eng |
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Optimization
2021
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| Truy cập trực tuyến: | https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1939698?journalCode=gopt20 https://dlib.phenikaa-uni.edu.vn/handle/PNK/2822 https://doi.org/10.1080/02331934.2021.1939698 |
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oai:localhost:PNK-28222022-08-17T05:54:37Z On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control Vu Huu Nhu optimal control Non-smooth semilinear elliptic equation control constraints This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus the associated control-to-state operator is, in general, not Gâteaux-differentiable. In addition to standing assumptions, two main hypotheses are imposed. The first one is the Gâteaux-differentiability at the considered control of the objective functional and it is precisely characterized by the vanishing of an adjoint state on the set of all zeros of the corresponding state. The second one is a structural assumption on the sets of all points at which the values of the interested state are ‘close’ to the non-differentiability point of the max-function. We then derive a ‘no-gap’ theory of second-order optimality conditions in terms of a second-order generalized derivative of the cost functional, i.e. for which the only change between necessary and sufficient second-order optimality conditions are between a strict and non-strict inequality. 2021-09-13T04:24:48Z 2021-09-13T04:24:48Z 2021 Bài trích https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1939698?journalCode=gopt20 https://dlib.phenikaa-uni.edu.vn/handle/PNK/2822 https://doi.org/10.1080/02331934.2021.1939698 eng Optimization |
| institution |
Digital Phenikaa |
| collection |
Digital Phenikaa |
| language |
eng |
| topic |
optimal control Non-smooth semilinear elliptic equation control constraints |
| spellingShingle |
optimal control Non-smooth semilinear elliptic equation control constraints Vu Huu Nhu On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| description |
This work is concerned with second-order necessary and sufficient optimality conditions for optimal control of a non-smooth semilinear elliptic partial differential equation, where the nonlinearity is the non-smooth max-function and thus the associated control-to-state operator is, in general, not Gâteaux-differentiable. In addition to standing assumptions, two main hypotheses are imposed. The first one is the Gâteaux-differentiability at the considered control of the objective functional and it is precisely characterized by the vanishing of an adjoint state on the set of all zeros of the corresponding state. The second one is a structural assumption on the sets of all points at which the values of the interested state are ‘close’ to the non-differentiability point of the max-function. We then derive a ‘no-gap’ theory of second-order optimality conditions in terms of a second-order generalized derivative of the cost functional, i.e. for which the only change between necessary and sufficient second-order optimality conditions are between a strict and non-strict inequality. |
| format |
Bài trích |
| author |
Vu Huu Nhu |
| author_facet |
Vu Huu Nhu |
| author_sort |
Vu Huu Nhu |
| title |
On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| title_short |
On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| title_full |
On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| title_fullStr |
On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| title_full_unstemmed |
On the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| title_sort |
on the no-gap second-order optimality conditions for a non-smooth semilinear elliptic optimal control |
| publisher |
Optimization |
| publishDate |
2021 |
| url |
https://www.tandfonline.com/doi/abs/10.1080/02331934.2021.1939698?journalCode=gopt20 https://dlib.phenikaa-uni.edu.vn/handle/PNK/2822 https://doi.org/10.1080/02331934.2021.1939698 |
| _version_ |
1751856264142389248 |
| score |
8.881002 |