A semi-smooth Newton method for solving elliptic equations with gradient constraints

DOI10.1051/m2an:2008049zbMath1161.65338OpenAlexW2139188758MaRDI QIDQ3623228

Karl Kunisch, Roland Griesse

Publication date: 16 April 2009

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/194449

zbMATH Keywords

regularizationnumerical exampleselliptic equationssemi-smooth Newton methodactive set strategygradient constraintsprimal-dual active set method

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

Primal-dual methods for the computation of trading regions under proportional transaction costs, A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state, A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables, A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints, Uzawa-type iterative solution methods for constrained saddle point problems, A direct algorithm in some free boundary problems, Finite element approximation and iterative method solution of elliptic control problem with constraints to gradient of state

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Optimal investment and consumption with transaction costs
• Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations
• Linear and quasilinear elliptic equations
• Boundary regulatity and uniqueness for an elliptic equations with gradient constraint
• PDE-Constrained Optimization Subject to Pointwise Constraints on the Control, the State, and Its Derivative
• A second order elliptic equation with gradient constraint
• The C^1,1—character of solutions of second order elliptic equations with gradient constraint
• Elliptic Partial Differential Equations of Second Order
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• The Primal-Dual Active Set Method for Nonlinear Optimal Control Problems with Bilateral Constraints
• Trading Regions Under Proportional Transaction Costs