2022/08/07 by Goldammer, Nico, Schulz, Volker H., Welker, Kathrin
#35Q93 #49J40 #49Q10 #65K15 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2208.03687
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.