A Riemannian View on Shape Optimization

Abstract

Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective. A Riemannian shape Hessian is defined yielding often sought properties like symmetry and quadratic convergence for Newton optimization methods.Comment: 15 pages, 1 figure, 1 table. Forschungsbericht / Universit\"at Trier, Mathematik, Informatik 2012,