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Solving differential Riccati equations: a nonlinear space-time method using tensor trains - MaRDI portal

Solving differential Riccati equations: a nonlinear space-time method using tensor trains (Q2061362)

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English	Solving differential Riccati equations: a nonlinear space-time method using tensor trains	scientific article

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scholarly article

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Solving differential Riccati equations: a nonlinear space-time method using tensor trains (English)

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Sergey V. Dolgov

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Numerical Algebra, Control and Optimization

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publication date

13 December 2021

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full work available at URL

https://arxiv.org/abs/1912.06944

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zbMATH Keywords

optimal control

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low-rank methods

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Riccati equations

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nonlinear problems

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MaRDI profile type

MaRDI publication profile

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Matrix Riccati equations in control and systems theory

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Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems

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A projection method to solve linear systems in tensor format

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RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations

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A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems

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Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data

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Rosenbrock Methods for Solving Riccati Differential Equations

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Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

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Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey

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Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

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Two-Level QTT-Tucker Format for Optimized Tensor Calculus

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Low-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes Equations

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TT-GMRES: solution to a linear system in the structured tensor format

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Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions

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Inexact Kleinman–Newton Method for Riccati Equations

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A Multigrid Method to Solve Large Scale Sylvester Equations

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A literature survey of low-rank tensor approximation techniques

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Tensor Spaces and Numerical Tensor Calculus

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Approximate iterations for structured matrices

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Convergence Analysis for Splitting of the Abstract Differential Riccati Equation

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Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints

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The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format

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Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays

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Order Reduction Methods for Solving Large-Scale Differential Matrix Riccati Equations

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Tensor Decompositions and Applications

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Analysis of Krylov subspace approximation to large-scale differential Riccati equations

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Krylov Subspace Methods for Linear Systems with Tensor Product Structure

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On the benefits of the \(L D L^T\) factorization for large-scale differential matrix equation solvers

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A new subspace iteration method for the algebraic Riccati equation

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Numerical low-rank approximation of matrix differential equations

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DMRG approach to fast linear algebra in the TT-format

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Tensor-Train Decomposition

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Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions

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Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function

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Sparse, adaptive Smolyak quadratures for Bayesian inverse problems

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Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations

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Singular Value Decay of Operator-Valued Differential Lyapunov and Riccati Equations

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A Low-Rank in Time Approach to PDE-Constrained Optimization

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Identifiers

zbMATH Open document ID

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10.3934/naco.2020034

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2061362

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