Gâteaux semiderivative approach applied to shape optimization for contact problems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916282096418816 |
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| author | Goldammer, Nico Schulz, Volker H. Welker, Kathrin |
| author_facet | Goldammer, Nico Schulz, Volker H. Welker, Kathrin |
| contents | Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs as well as distributed, non-linear, non-convex and infinite-dimensional aspects due to the shapes which complicate to set up an optimality system and, thus, to develop efficient solution algorithms. In this paper, we consider Gâteaux semiderivatives in order to formulate optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the contact problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_03687 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Gâteaux semiderivative approach applied to shape optimization for contact problems Goldammer, Nico Schulz, Volker H. Welker, Kathrin Optimization and Control 49Q10, 49J40, 35Q93, 65K15 Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs as well as distributed, non-linear, non-convex and infinite-dimensional aspects due to the shapes which complicate to set up an optimality system and, thus, to develop efficient solution algorithms. In this paper, we consider Gâteaux semiderivatives in order to formulate optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the contact problem. |
| title | Gâteaux semiderivative approach applied to shape optimization for contact problems |
| topic | Optimization and Control 49Q10, 49J40, 35Q93, 65K15 |
| url | https://arxiv.org/abs/2208.03687 |