A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems

DOI10.1007/s10898-014-0206-yzbMath1339.49025OpenAlexW1998163691MaRDI QIDQ280973

Mingqing Xiao, Jun Liu

Publication date: 10 May 2016

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-014-0206-y

zbMATH Keywords

optimal controllinear multigridsemi-smooth Newton methodcollective Jacobi smootherfirst order necessary optimality systemsfull-approximation storage multigridsemi-linear elliptic PDE

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Numerical methods based on necessary conditions (49M05) Newton-type methods (49M15) Discrete approximations in optimal control (49M25) Semilinear elliptic equations (35J61)

Related Items

Smoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control Problems ⋮ A leapfrog multigrid algorithm for the optimal control of parabolic PDEs with Robin boundary conditions ⋮ A global convergent semi-smooth Newton method for semi-linear elliptic optimal control problem ⋮ A new multigrid method for unconstrained parabolic optimal control problems ⋮ A leapfrog semi-smooth Newton-multigrid method for semilinear parabolic optimal control problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence analysis of multigrid methods with collective point smoothers for optimal control problems
• A multigrid method for constrained optimal control problems
• A mesh-independence result for semismooth Newton methods.
• Fast solution of elliptic control problems
• A multigrid scheme for elliptic constrained optimal control problems
• High-order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems
• Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems
• Error estimates for the numerical approximation of a semilinear elliptic control problem
• Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems
• Convergence Analysis of All-at-Once Multigrid Methods for Elliptic Control Problems under Partial Elliptic Regularity
• The semi-smooth Newton method for variationally discretized control constrained elliptic optimal control problems; implementation, convergence and globalization
• Nonlinear Partial Differential Equations for Scientists and Engineers
• A Robust Multigrid Method for Elliptic Optimal Control Problems
• Computational Optimization of Systems Governed by Partial Differential Equations
• Second Order Analysis for Bang-Bang Control Problems of PDEs
• Numerical solution of saddle point problems
• Lagrange Multiplier Approach to Variational Problems and Applications
• Optimization with PDE Constraints
• Multigrid Methods for PDE Optimization
• Inexact Newton Methods
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Primal-Dual Strategy for Constrained Optimal Control Problems
• Fast Iterative Solution of Stabilised Stokes Systems Part II: Using General Block Preconditioners
• Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• On Mesh-Independent Convergence of an Inexact Newton--Multigrid Algorithm
• A Multigrid Tutorial, Second Edition
• Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
• Iterative Solution of Nonlinear Equations in Several Variables
• A globalization strategy for the multigrid solution of elliptic optimal control problems