scholarly journals Existence and Relaxation for Finite-Dimensional Optimal Control Problems Driven by Maximal Monotone Operators

2003 ◽  
pp. 863-898
Author(s):  
Nikolaos Papageorgiou ◽  
Francesca Papalini
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Control Problems ◽  
Finite Dimensional

Geometric Convergence of Iterative Methods for a Problem with M-matrices and Diagonal Multivalued Operators

2002 ◽  
Vol 2 (1) ◽  
pp. 26-40 ◽  
Author(s):  
Alexander Lapin
Keyword(s):  
Iterative Methods ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Mesh Approximation ◽  
Finite Dimensional ◽  
Multivalued Operators ◽  
Geometric Convergence ◽  
Parallel Iterative ◽  
A Free Boundary Problem

Abstract A finite-dimensional problem with several M-matrices and diagonal maximal monotone operators is studied. This problem includes variational inequalities with M-matrices as a partial case and appears, in particular, as a mesh approximation for a free boundary problem with several constraints and nonlinear relations. The existence of an unique solution for the problem is studied, as well as the convergence and geometric rate of the convergence for a class of the iterative methods, the Schwarz alternating-type methods among them. The application of the general results to a mesh scheme for a dam problem is considered. Parallel iterative methods are constructed on the basis of the domain decomposition, geometric convergence of these methods is justified.

On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems

2010 ◽  
Vol 10 (3) ◽  
pp. 283-301 ◽  
Author(s):  
E. Laitinen ◽  
A. Lapin ◽  
S. Lapin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Function ◽  
Elliptic Boundary ◽  
Iterative Algorithms ◽  
Iterative Solution ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Finite Dimensional ◽  
The Right

AbstractIterative methods for finite-dimensional inclusions which arise in applying a finite-element or a finite-difference method to approximate state-constrained optimal control problems have been investigated. Specifically, problems of control on the right- hand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergence for the iterative algorithms based on the finding of the control function or Lagrange multipliers are proved.

scholarly journals On the convergence of min/sup points in optimal control problems

2001 ◽  
Vol 6 (1) ◽  
pp. 35-52
Author(s):  
Adib Bagh
Keyword(s):  
Optimal Control ◽  
Large Class ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Finite Dimensional ◽  
Lopsided Convergence ◽  
Definition Of ◽  
Stability Results ◽  
Convex Control

We modify the definition of lopsided convergence of bivariate functionals to obtain stability results for the min/sup points of some control problems. In particular, we develop a scheme of finite dimensional approximations to a large class of non-convex control problems.

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