A Riemannian View on Shape Optimization
Shape optimization based on the shape calculus is numerically mostly performed using steepest descent methods. This paper provides a novel framework for analyzing shape Newton optimization methods by exploiting a Riemannian perspective. A Riemannian shape Hessian is defined possessing often sought properties like symmetry and quadratic convergence for Newton optimization methods.
shape optimization riemannian manifold newton method 49q10 49m15 53b20