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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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Main Author: Vu Huu Nhu
Format: Bài trích
Language:eng
Published: Optimization 2021
Subjects:
optimal control
Non-smooth semilinear elliptic equation
control constraints
Online Access: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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spelling 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
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score 8.881002

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