Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs
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Publication:2954481
DOI10.1137/16M1057607zbMath1381.49027MaRDI QIDQ2954481
Michael Ulbrich, Sebastian Garreis
Publication date: 13 January 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
nonlinear optimizationparametric variational inequalitiesinterior point methodsuncertainty quantificationsemismooth Newton methodslow-rank tensorsoptimal control under uncertaintyPDEs with uncertainties
Numerical mathematical programming methods (65K05) Newton-type methods (49M15) Stochastic programming (90C15) Multilinear algebra, tensor calculus (15A69) Numerical methods for variational inequalities and related problems (65K15)
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Uses Software
Cites Work
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- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- TT-cross approximation for multidimensional arrays
- Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats
- The geometry of algorithms using hierarchical tensors
- Low-rank tensor completion by Riemannian optimization
- Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
- Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- Adaptive near-optimal rank tensor approximation for high-dimensional operator equations
- Approximate iterations for structured matrices
- Global optimization by multilevel coordinate search
- Inexact interior-point method
- Computations in quantum tensor networks
- A new scheme for the tensor representation
- Optimization on the hierarchical Tucker manifold - applications to tensor completion
- A nonsmooth version of Newton's method
- DMRG approach to fast linear algebra in the TT-format
- Analysis of Inexact Trust-Region SQP Algorithms
- Adaptive low-rank methods for problems on Sobolev spaces with error control in L2
- Riemannian Optimization for High-Dimensional Tensor Completion
- On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format
- A literature survey of low-rank tensor approximation techniques
- The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
- Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
- Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization
- Hierarchical Singular Value Decomposition of Tensors
- A polynomial chaos approach to stochastic variational inequalities
- Tensor Spaces and Numerical Tensor Calculus
- Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
- Hierarchical Tensor Approximation of Output Quantities of Parameter-Dependent PDEs
- Optimization with PDE Constraints
- Globally Convergent Inexact Newton Methods
- Semismooth Newton Methods for Operator Equations in Function Spaces
- The Primal-Dual Active Set Strategy as a Semismooth Newton Method
- A Multilinear Singular Value Decomposition
- An Introduction to Variational Inequalities and Their Applications
- Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
- Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix
- Inexact Objective Function Evaluations in a Trust-Region Algorithm for PDE-Constrained Optimization under Uncertainty
- Algorithm 941
- Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
- Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure
- Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk