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.

15 pages, 1 figure, 1 table. Forschungsbericht / Universität Trier, Mathematik, Informatik 2012, 1

References in corpus (2)

• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Sobolev metrics on shape space of surfaces

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