Nonsmooth Newton Methods for Set-Valued Saddle Point Problems

DOI10.1137/060671012zbMath1190.49035OpenAlexW2048992868MaRDI QIDQ3559146

Ralf Kornhuber, Carsten Gräser

Publication date: 11 May 2010

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/060671012

zbMATH Keywords

nonsmooth Newton methodsUzawa algorithmsactive set preconditionersset-valued saddle point problems

Mathematics Subject Classification ID

Numerical methods involving duality (49M29) Optimality conditions and duality in mathematical programming (90C46) Newton-type methods (49M15) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (12)

The semi-smooth Newton method for variationally discretized control constrained elliptic optimal control problems; implementation, convergence and globalization ⋮ Numerical approximation of multi-phase Penrose-Fife systems ⋮ Preconditioned Uzawa-type method for a state constrained parabolic optimal control problem with boundary control ⋮ Phase field computations for surface diffusion and void electromigration in \({\mathbb{R}^3}\) ⋮ Method of penalization for the state equation for an elliptical optimal control problem ⋮ Optimal distributed control of nonlinear Cahn-Hilliard systems with computational realization ⋮ An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system ⋮ Iterative solution methods for mesh approximation of control and state constrained optimal control problem with observation in a part of the domain ⋮ Uzawa-type iterative solution methods for constrained saddle point problems ⋮ An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem ⋮ Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method ⋮ Iterative Solution Methods for Large-Scale Constrained Saddle-Point Problems

Uses Software

• NewtonLib

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