Uzawa-type iterative solution methods for constrained saddle point problems
type: Item
instance of: scholarly article
title: Uzawa-type iterative solution methods for constrained saddle point problems
zbMATH Open document ID: 1472.49016
DOI: 10.1134/S1995080218050098
published in: Lobachevskii Journal of Mathematics
publication date: 2018-09-27T00:00:00Z
review text: The paper deals with the iterative solution of saddle point problems in finite dimensional real valued spaces. It summarizes the general theory developed by the author with co-authors in the last years. For finite-dimensional saddle point problem with a nonlinear monotone operator and constraints, iterative methods are knows, which can be viewed as preconditioned Uzawa methods or as Uzawa-block relaxation methods. In the first section the author gives some general results on the solvability of problem the considered problem and the convergence of iterative methods. These results are based on three articles from the author and coworkers from the last years. In the following sections some application on the finite element/finete differences discretization of elliptic and parabolic PDEs optimal control problems and the resulting (optimality) conditions, i.e. saddle point problems are considered. When applying iterative method to such problems, one problem is to construct suitable preconditioners that ensure the convergence and effective implementation of iterative methods and to obtain the admissible intervals of iterative parameters which do not depend on mesh parameters. The choice of preconditioners is handled case by case for the considered example problems.
reviewed by: Uwe Prüfert
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 65K15
Mathematics Subject Classification ID: 49M20
zbMATH DE Number: 6945066
zbMATH Keywords: constrained saddle point problems
zbMATH Keywords: variational inequalities
zbMATH Keywords: optimal control problems
zbMATH Keywords: state and control constraints
author: A. V. Lapin
MaRDI profile type: Publication
cites work: Q3914338
cites work: Q3995612
cites work: Q3511010
cites work: The convergence of an interior point method for an elliptic control problem with mixed control-state constraints
cites work: A regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraints
cites work: Nonsmooth Newton Methods for Set-Valued Saddle Point Problems
cites work: A semi-smooth Newton method for solving elliptic equations with gradient constraints
cites work: Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient State Constraints
cites work: Variational discretization of a parabolic control problem in the presence of pointwise state constraints
cites work: Numerical solution of saddle point problems
cites work: On the iterative solution methods for finite-dimensional inclusions with applications to optimal control problems
cites work: Preconditioned Uzawa-type methods for finite-dimensional constrained saddle point problems
cites work: State-constrained optimal control of an elliptic equation with its right-hand side used as control function
cites work: Iterative solution methods for variational inequalities with nonlinear main operator and constraints to gradient of solution
cites work: Iterative Solution Methods for Large-Scale Constrained Saddle-Point Problems
cites work: Iterative solution methods for mesh approximation of control and state constrained optimal control problem with observation in a part of the domain
cites work: Efficiently implementable iterative methods for linear elliptic variational inequalities with constraints on the gradient of solution
cites work: Easily implementable iterative methods for variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution
cites work: Finite element approximation and iterative method solution of elliptic control problem with constraints to gradient of state
cites work: Using domain decomposition method and non-matching grids for solving some variational inequalities
cites work: Explicit algorithms to solve a class of state constrained parabolic optimal control problems
cites work: Preconditioned Uzawa-type method for a state constrained parabolic optimal control problem with boundary control
cites work: Solution of elliptic optimal control problem with pointwise and non-local state constraints
cites work: Domain decomposition and Uzawa-type iterative method for elliptic variational inequality
cites work: Q4085497
cites work: Q4162607
cites work: Q5562267
cites work: Q3521017
full work available at URL: s1995080218050098
OpenAlex ID: W2836727598
description: scientific article; zbMATH DE number 6945066