Properties of Projection and Penalty Methods for Discretized Elliptic Control Problems
نویسندگان
چکیده
In this paper, properties of projection and penalty methods are studied in connection with control problems and their discretizations. In particular, the convergence of an interior-exterior penalty method applied to simple state constraints as well as the contraction behavior of projection mappings are analyzed. In this study, the focus is on the application of these methods to discretized control problem.
منابع مشابه
Preconditioned Solution of State Gradient Constrained Elliptic Optimal Control Problems
Elliptic optimal control problems with pointwise state gradient constraints are considered. A quadratic penalty approach is employed together with a semismooth Newton iteration. Three different preconditioners are proposed and the ensuing spectral properties of the preconditioned linear Newton saddle-point systems are analyzed in dependence on the penalty parameter. A new bound for the smallest...
متن کاملA link between local projection stabilizations and the continuous interior penalty method for convection-diffusion problems
We study stabilization methods for the discretization of convection-dominated elliptic convection-diffusion problems by linear finite elements. It turns out that there exist close relations between a new version of stabilization via local projection and the continuous interior penalty method. AMS Subject Classifications: 65 N15, 65N30, 65N12
متن کاملOptimal Penalty-feti Method for Variational Inequalities
We shall first briefly review our results related to solving of the convex box constrained quadratic programming problems by combination of the active set strategy and the conjugate gradient method with projections [1]. In particular, we shall show that with proper modification of the proportioning algorithm with projection [2], it is possible give the rate of convergence in terms of the spectr...
متن کاملOn Least-squares Variational Principles for the Discretization of Optimization and Control Problems
The approximate solution of optimization and control problems for systems governed by linear, elliptic partial differential equations is considered. Such problems are most often solved using methods based on the application of the Lagrange multiplier rule followed by discretization through, e.g., a Galerkin finite element method. As an alternative, we show how least-squares finite element metho...
متن کاملElliptic Control by Penalty Techniques with Control Reduction
The paper deals with the numerical treatment of optimal control problems with bounded distributed controls and elliptic state equations by a wider class of barrier-penalty methods. If the constraints are treated by barrier-penalty techniques then the necessary and sufficient optimality condition forms a coupled system of nonlinear equations which contain not only the usual adjoint and the state...
متن کامل