A Riemannian View on Shape Optimization
Optimization and Control
2014-05-14 v2
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.
Cite
@article{arxiv.1203.1493,
title = {A Riemannian View on Shape Optimization},
author = {Volker Schulz},
journal= {arXiv preprint arXiv:1203.1493},
year = {2014}
}
Comments
15 pages, 1 figure, 1 table. Forschungsbericht / Universit\"at Trier, Mathematik, Informatik 2012, 1