A Riemannian View on Shape Optimization

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 p...

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Bibliographic Details
Published inFoundations of computational mathematics Vol. 14; no. 3; pp. 483 - 501
Main Author Schulz, Volker H.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2014
Springer
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus
Computer Science
Convergence
Economics
Foundations
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematical analysis
Mathematical models
Mathematical optimization
Mathematical research
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Optimization
Optimization techniques
Riemann integral
Shape optimization
Steepest descent method
53B20
49M15
Riemannian manifold
49Q10
Newton method
Shape optimization
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Summary: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.
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ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-014-9200-5