G\^ateaux semiderivative approach applied to shape optimization for contact problems
Optimization and Control
2024-06-12 v3
Abstract
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 G\^ateaux semiderivatives in order to formulate optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the contact problem.
Cite
@article{arxiv.2208.03687,
title = {G\^ateaux semiderivative approach applied to shape optimization for contact problems},
author = {Nico Goldammer and Volker H. Schulz and Kathrin Welker},
journal= {arXiv preprint arXiv:2208.03687},
year = {2024}
}