Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization
From MaRDI portal
Publication:4638921
DOI10.1080/10556788.2017.1314471zbMath1388.35036arXiv1604.05017OpenAlexW2964170750MaRDI QIDQ4638921
Publication date: 2 May 2018
Published in: Optimization Methods and Software (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.05017
Optimization of shapes other than minimal surfaces (49Q10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) First-order elliptic systems (35J46)
Related Items
Uncertainty quantification for kinetic models in socio-economic and life sciences ⋮ Uncertainty quantification for kinetic equations ⋮ Two-Dimensional Shape Optimization with Nearly Conformal Transformations ⋮ Reproducing kernels: harmonic analysis and some of their applications ⋮ Analyzing Smooth and Singular Domain Perturbations in Level Set Methods ⋮ Shape Optimization for the $$\text {SP}_1$$-Model for Convective Radiative Heat Transfer ⋮ Diffusive Radiation Models for Optimal Shape Design in Phosphate Production ⋮ Shape Optimization with Nonsmooth Cost Functions: From Theory to Numerics ⋮ Weighted p-regular kernels for reproducing kernel Hilbert spaces and Mercer Theorem ⋮ Energy-efficient high temperature processes via shape optimization ⋮ Weakly Normal Basis Vector Fields in RKHS with an Application to Shape Newton Methods ⋮ Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains ⋮ A novel W1,∞ approach to shape optimisation with Lipschitz domains
Cites Work
- Unnamed Item
- Unnamed Item
- An optimal triangulation for second-order elliptic problems
- A level-set method for shape optimization.
- Level set methods and dynamic implicit surfaces
- Comparison of approximate shape gradients
- Variation and optimization of formes. A geometric analysis
- Riemannian geometries on spaces of plane curves
- Distributed shape derivativeviaaveraged adjoint method and applications
- Shapes and Geometries
- On a Bernoulli problem with geometric constraints
- VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM
- Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
- A Unified Discrete–Continuous Sensitivity Analysis Method for Shape Optimization
- Shape Methods for the Transmission Problem with a Single Measurement
- On Convergence in Elliptic Shape Optimization
- Minimax Lagrangian Approach to the Differentiability of Nonlinear PDE Constrained Shape Functions Without Saddle Point Assumption
- Theory of Reproducing Kernels
- Scattered Data Approximation
- Shapes and diffeomorphisms
