Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics

Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification efficient algorithms. In this paper we propose investigate nonlinear conjugate gradient methods Steklov-Poincar\'e-type metrics for solution problems constrained by partial differential equations. We embed these into general algorithmic framework gradient-based discuss numerical discretization numerically compare proposed to already established descent limited memory BFGS several benchmark problems. The results show that perform well practice they are an attractive addition