We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth
function f, not necessarily convex. We introduce an inexact line search that generates a …

We propose in this paper two kinds of continuity preserving discrete shape gradients of
boundary type for PDE-constrained shape optimizations. First, a modified boundary shape …

The optimization of shape functionals under convexity, diameter or constant width
constraints shows numerical challenges. The support function can be used in order to …

We develop a computational method for extremal Steklov eigenvalue problems and apply it
to study the problem of maximizing the p th Steklov eigenvalue as a function of the domain …

Recently Fraser and Schoen showed that the solution of a certain extremal Steklov
eigenvalue problem on a compact surface with boundary can be used to generate a free …

We develop methods based on fundamental solutions to compute the Steklov, Wentzell and
Laplace–Beltrami eigenvalues in the context of shape optimization. In the class of smooth …

In this paper we consider the problem of maximizing the k th Steklov eigenvalue of the
Laplacian (or a more general spectral functional), among all sets of \mathbbR^d of …

Let (M, g) be a connected, closed, orientable Riemannian surface and denote by λk (M, g)
the kth eigenvalue of the Laplace− Beltrami operator on (M, g). In this paper, we consider the …

In this paper, by mainly using the rearrangement technique and suitably constructing trial
functions, under the constraint of fixed weighted volume, we can successfully obtain several …

In this work we address the application of the method of fundamental solution (MFS) as a
forward solver in some shape optimization problems in two-and three-dimensional domains …