Smoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control Problems

Publication date: 30 March 2023

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13066

zbMATH Keywords

multigrid local Fourier analysis semismooth Newton method smoothing factor Braess-Sarazin relaxation collective Jacobi relaxation

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Optimality conditions for problems involving partial differential equations (49K20) Newton-type methods (49M15) Methods involving semicontinuity and convergence; relaxation (49J45) Iterative numerical methods for linear systems (65F10) Discrete approximations in optimal control (49M25)

Uses Software

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems
Convergence analysis of multigrid methods with collective point smoothers for optimal control problems
A multigrid method for constrained optimal control problems
A mixed finite element scheme for optimal control problems with pointwise state constraints
Block preconditioners for elliptic PDE-constrained optimization problems
A mesh-independence result for semismooth Newton methods.
A multigrid scheme for elliptic constrained optimal control problems
Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems
Estimates for multigrid methods based on red-black Gauss-Seidel smoothings
Preconditioning PDE-constrained optimization with \(L^1\)-sparsity and control constraints
An efficient duality-based approach for PDE-constrained sparse optimization
An FE-inexact heterogeneous ADMM for elliptic optimal control problems with \(L^1\)-control cost
Inexact Newton methods for solving nonsmooth equations
A multi-level ADMM algorithm for elliptic PDE-constrained optimization problems
A novel multigrid method for elliptic distributed control problems
Novel mass-based multigrid relaxation schemes for the Stokes equations
A local Fourier convergence analysis of a multigrid method using symbolic computation
Optimal-Order Preconditioners for Linear Systems Arising in the Semismooth Newton Solution of a Class of Control-Constrained Problems
Convergence Analysis of All-at-Once Multigrid Methods for Elliptic Control Problems under Partial Elliptic Regularity
Closed-form multigrid smoothing factors for lexicographic Gauss-Seidel
Optimal Solvers for PDE-Constrained Optimization
Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints
Black Box Multigrid with coarsening by a factor of three
A Robust Multigrid Method for Elliptic Optimal Control Problems
Computational Optimization of Systems Governed by Partial Differential Equations
Lagrange Multiplier Approach to Variational Problems and Applications
Optimization with PDE Constraints
Multigrid solution of the optical flow system using a combined diffusion‐ and curvature‐based regularizer
Multigrid Methods for PDE Optimization
Primal-Dual Strategy for Constrained Optimal Control Problems
Accuracy and Convergence Properties of the Finite Difference Multigrid Solution of an Optimal Control Optimality System
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
Fourier Analysis of Periodic Stencils in Multigrid Methods
A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems
A two‐phase strategy for control constrained elliptic optimal control problems
Multigrid Smoothing Factors for Red-Black Gauss–Seidel Relaxation Applied to a Class of Elliptic Operators
Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems
Nonsymmetric Black Box multigrid with coarsening by three
A new preconditioning approach for an interior point‐proximal method of multipliers for linear and convex quadratic programming
A New Convergence Analysis of Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints
Operator Preconditioning for a Class of Inequality Constrained Optimal Control Problems
Optimal Complex Relaxation Parameters in Multigrid for Complex-Shifted Linear Systems
Interior‐point methods and preconditioning for PDE‐constrained optimization problems involving sparsity terms
On Local Fourier Analysis of Multigrid Methods for PDEs with Jumping and Random Coefficients
Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls
P 1 finite element methods for an elliptic optimal control problem with pointwise state constraints
Transforming smoothers for PDE constrained optimization problems

This page was built for publication: Smoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control Problems