A Riemannian View on Shape Optimization

Details A Riemannian View on Shape Optimization A Riemannian View on Shape Optimization

2012-03-07

arxiv.org/abs/1203.1493v1

Mathematics

Optimization and Control

14 pages, 1 figurem 1 table

Scientific paper

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.

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