Towards a Lagrange-Newton approach for PDE constrained shape optimization

TL;DR

This paper extends a Riemannian framework for shape optimization to a Lagrange-Newton method, enabling more efficient PDE constrained shape optimization by leveraging geometric structures.

Contribution

It introduces a Lagrange-Newton approach on Riemannian vector bundles for PDE constrained shape optimization, expanding previous Riemannian methods.

Findings

Extension of Riemannian shape optimization to Lagrange-Newton methods

Implementation demonstrated on a simple numerical example

Potential for improved efficiency in PDE constrained shape optimization

Abstract

The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space bundles and exemplified for a simple numerical example.