Abstract
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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Acknowledgments
The author is very grateful to Oliver Roth (University of Würzburg, Germany) for calling the author’s attention to the publication [34], which prompted the whole endeavor of this paper. Furthermore, I would like to thank the three anonymous referees, who helped to polish the paper significantly.
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Communicated by Michael Todd.
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Schulz, V.H. A Riemannian View on Shape Optimization. Found Comput Math 14, 483–501 (2014). https://doi.org/10.1007/s10208-014-9200-5
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DOI: https://doi.org/10.1007/s10208-014-9200-5