Directional differentiability for shape optimization with variational inequalities as constraints Full article
| Journal |
ESAIM: Control, Optimisation and Calculus of Variations
ISSN: 1292-8119 |
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| Output data | Year: 2023, Volume: 29, Article number : 64, Pages count : 30 DOI: 10.1051/cocv/2023056 | ||||
| Tags | OPTIMAL CONTROL, SHAPE OPTIMIZATION, VARIATIONAL INEQUALITY, PENALIZATION, LAGRANGE METHOD, LAVRENTIEV REGULARIZATION, FREE DISCONTINUITY, NON-PENETRATING CRACK | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2021-0010 |
Abstract:
For equilibrium constrained optimization problems subject to nonlinear state equations,
the property of directional differentiability with respect to a parameter is studied. An abstract class
of parameter dependent shape optimization problems is investigated with penalty constraints linked
to variational inequalities. Based on the Lagrange multiplier approach, on smooth penalties due to
Lavrentiev regularization, and on adjoint operators, a shape derivative is obtained. The explicit formula
provides a descent direction for the gradient algorithm identifying the shape of the breaking-line from
a boundary measurement. A numerical example is presented for a nonlinear Poisson problem modeling
Barenblatt’s surface energies and non-penetrating cracks.
Cite:
Kovtunenko V.A.
, Kunisch K.
Directional differentiability for shape optimization with variational inequalities as constraints
ESAIM: Control, Optimisation and Calculus of Variations. 2023. V.29. 64 :1-30. DOI: 10.1051/cocv/2023056 WOS Scopus РИНЦ OpenAlex
Directional differentiability for shape optimization with variational inequalities as constraints
ESAIM: Control, Optimisation and Calculus of Variations. 2023. V.29. 64 :1-30. DOI: 10.1051/cocv/2023056 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jan 30, 2023 |
| Accepted: | Jul 19, 2023 |
| Published print: | Aug 8, 2023 |
Identifiers:
| Web of science: | WOS:001044087500001 |
| Scopus: | 2-s2.0-85168729629 |
| Elibrary: | 60776344 |
| OpenAlex: | W4384927682 |