A Riemannian View on Shape Optimization

作者：Schulz Volker H^*

来源：Foundations of Computational Mathematics, 2014, 14(3): 483-501.

DOI：10.1007/s10208-014-9200-5

• Shape optimization
• Riemannian manifold
• Newton method

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.

• 出版日期2014-6