Hamburger Beiträge zur Angewandten Mathematik Variational Discretization of Lavrentiev - Regularized State Constrained Elliptic Control Problems

Hamburger Beiträge zur Angewandten Mathematik Continuous Convergence of Relations - A Principle in Discretization Procedures

Hamburger Beiträge zur Angewandten Mathematik A Posteriori Error Representations for Elliptic Optimal Control Problems with Control and State Constraints

In this work we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. Building upon the concept proposed in [9] the algorithm applies a Moreau-Yosida regularization technique for handling state constraints. The state and co-state variables are discretized using continuous piecewise linear finite elements while a ...

Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems

A class of nonlinear elliptic optimal control problems with mixed control-state constraints arising, e.g., in Lavrentiev-type regularized state constrained optimal control is considered. Based on its first order necessary optimality conditions, a semismooth Newton method is proposed and its fast local convergence in function space as well as a mesh-independence principle for appropriate discret...

Hamburger Beiträge zur Angewandten Mathematik A Priori Error Estimates for a Finite Element Discretization of Parabolic Optimization Problems with Pointwise Constraints in Time on Mean Values of the Gradient of the State

This article is concerned with the discretization of parabolic optimization problems subject to pointwise in time constraints on mean values of the derivative of the state variable. Central component of the analysis are a priori error estimates for the dG(0)-cG(1) discretization of the parabolic partial differential equation (PDE) in the L∞(0, T ;H1 0 (Ω))-norm, together with corresponding esti...

Mesh Independence and Fast Local Convergence of a Primal-dual Active-set Method for Mixed Control-state Constrained Elliptic Control Problems

A class of mixed control-state constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentiev-type regularized state constrained optimal control is considered. Its numerical solution is obtained via a primal-dual activeset method, which is equivalent to a class of semi-smooth Newton methods. The locally superlinear convergence of the active-...