3 papers
math.OC2016
Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation
Martin Eigel, Kevin Sturm
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of ke…
math.OC2016
A structure theorem for shape functions defined on submanifolds
K. Sturm
In this paper, we study shape functions depending on closed submanifolds. We prove a new structure theorem that establishes the general structure of the shape derivative for this t…
math.OC2016
Shape optimisation with nonsmooth cost functions: from theory to numerics
Kevin Sturm
This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-deriv…