Towards a Lagrange-Newton approach for PDE constrained shape   optimization
  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. 
Volker H. Schulz, Martin Siebenborn and Kathrin Welker
math.NA