Stochastic Approximation for Optimization in Shape Spaces

DOI10.1137/20M1316111zbMath1458.49034arXiv2001.10786OpenAlexW3123321780MaRDI QIDQ5147032

Estefanía Loayza-Romero, Caroline Geiersbach, Kathrin Welker

Publication date: 2 February 2021

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.10786

zbMATH Keywords

stochastic approximationshape optimizationstochastic gradient methodinterface identificationPDE-constrained optimization under uncertainty

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Optimization of shapes other than minimal surfaces (49Q10) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (7)

An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization ⋮ Performance Bounds for PDE-Constrained Optimization under Uncertainty ⋮ A stochastic projection and contraction algorithm with inertial effects for stochastic variational inequalities ⋮ A pessimistic bilevel stochastic problem for elastic shape optimization ⋮ Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints ⋮ Taylor Approximation for Chance Constrained Optimization Problems Governed by Partial Differential Equations with High-Dimensional Random Parameters ⋮ Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics

Cites Work

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• Computational comparison of surface metrics for PDE constrained shape optimization
• Functional and shape data analysis
• A Riemannian view on shape optimization
• Sobolev metrics on shape space of surfaces
• Worst-case shape optimization for the Dirichlet energy
• On geodesic exponential maps of the Virasoro group
• Semimartingales: A course on stochastic processes
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• The second order perturbation approach for elliptic partial differential equations on random domains
• On optimization transfer operators in shape spaces
• Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics
• Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces
• Stochastic subgradient method converges on tame functions
• Computational investigations of an obstacle-type shape optimization problem in the space of smooth shapes
• Topology optimization under uncertainty via non-intrusive polynomial chaos expansion
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Robust shape optimization of continuous structures via the level set method
• Riemannian geometries on spaces of plane curves
• Overview of the geometries of shape spaces and diffeomorphism groups
• Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle
• Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• An Introduction to Computational Stochastic PDEs
• Shape Optimization for Quadratic Functionals and States with Random Right-Hand Sides
• On Shape Optimization with Stochastic Loadings
• Lineare Funktionalanalysis
• Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
• Structured Inverse Modeling in Parabolic Diffusion Problems
• Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
• Variational approach to shape derivatives
• Shape Optimization Under Uncertainty—A Stochastic Programming Perspective
• Electrical Impedance Tomography
• Introduction to Riemannian Manifolds
• Stochastic Dominance Constraints in Elastic Shape Optimization
• Optimal Control of PDEs under Uncertainty
• Algorithmic Aspects of Multigrid Methods for Optimization in Shape Spaces
• An Effective Method for Parameter Estimation with PDE Constraints with Multiple Right-Hand Sides
• A deterministic approximation method in shape optimization under random uncertainties
• Incorporating knowledge on the measurement noise in electrical impedance tomography
• An Adaptive Stochastic Galerkin Tensor Train Discretization for Randomly Perturbed Domains
• Solving a Bernoulli type free boundary problem with random diffusion
• A Stochastic Gradient Method With Mesh Refinement for PDE-Constrained Optimization Under Uncertainty
• Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces
• Quantification of Airfoil Geometry-Induced Aerodynamic Uncertainties---Comparison of Approaches
• Stochastic Gradient Descent on Riemannian Manifolds
• Minimax Lagrangian Approach to the Differentiability of Nonlinear PDE Constrained Shape Functions Without Saddle Point Assumption
• A Stochastic Approximation Method
• Probability: A Graduate Course
• Shapes and diffeomorphisms

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