On computation of the shape Hessian of the cost functional without shape sensitivity of the state variable

DOI10.1007/s10957-013-0520-4zbMath1301.49117OpenAlexW2055465720MaRDI QIDQ462997

Karl Kunisch, Henry Kasumba

Publication date: 23 October 2014

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: http://unipub.uni-graz.at/doi/doi:10.1007/s10957-013-0520-4

zbMATH Keywords

cost functionalshape optimizationshape derivativeshape Hessian

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Sensitivity analysis for optimization problems on manifolds (49Q12) PDEs in connection with control and optimization (35Q93)

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Cites Work

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• Modelling and control in solid mechanics
• On the shape derivative for problems of Bernoulli type
• Anatomy of the shape Hessian
• Anatomy of the shape Hessian via Lie brackets
• Variational approach to shape derivatives for a class of Bernoulli problems
• Compressible Navier-Stokes Equations
• Variational approach to shape derivatives
• Finite Element Methods for Navier-Stokes Equations
• Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian
• Shape optimization and trial methods for free boundary problems
• Levenberg–Marquardt level set methods for inverse obstacle problems
• Introduction to Shape Optimization