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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Veröffentlicht in:	Foundations of computational mathematics 2014-06, Vol.14 (3), p.483-501
1. Verfasser:	Schulz, Volker H.
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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container_title	Foundations of computational mathematics
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description	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.
doi_str_mv	10.1007/s10208-014-9200-5
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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
title	A Riemannian View on Shape Optimization
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