Gâteaux semiderivative approach applied to shape optimization of obstacle problems

• Autorzy: Goldammer Nico , Schulz Volker H. , Welker Kathrin

Identyfikatory

DOI

10.2478/candc-2024-0007

• Języki publikacji: EN

Abstrakty

EN

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 setting up an optimality system and, thus, developing efficient solution algorithms. In this paper, we consider Gâteaux semiderivatives for the purpose of formulating optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the obstacle problem.

Słowa kluczowe

EN

obstacle problem; directional derivative; variational inequality; shape optimization; shape derivative; material derivative; optimality conditions; Gâteaux semiderivatives

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2024
• Tom: Vol. 53, No. 1
• Strony: 141--161
• Opis fizyczny: Bibliogr. 56 poz.

Twórcy

autor

Goldammer Nico

• Helmut-Schmidt-University / University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany

autor

Schulz Volker H.

• Trier University, Universitätsring 15, 54296 Trier, Germany

autor

Welker Kathrin

• Helmut-Schmidt-University / University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany

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