Second order optimality conditions and their role in PDE control

E Casas, F Tröltzsch - Jahresbericht der Deutschen Mathematiker …, 2015 - Springer
If f:R^n→R is twice continuously differentiable, f′(u)= 0 and f ″(u) is positive definite, then u
is a local minimizer of f. This paper surveys the extension of this well known second order …

[图书][B] Optimization with PDE constraints

M Hinze, R Pinnau, M Ulbrich, S Ulbrich - 2008 - books.google.com
Solving optimization problems subject to constraints given in terms of partial d-ferential
equations (PDEs) with additional constraints on the controls and/or states is one of the most …

[图书][B] Optimale Steuerung partieller Differentialgleichungen

F Tröltzsch - 2005 - Springer
Die mathematische Optimierung von Vorgängen, die durch partielle Differentialgleichungen
modelliert werden, hat in den letzten Jahren einen beachtlichen Aufschwung genommen …

Adaptive space-time finite element methods for parabolic optimization problems

D Meidner, B Vexler - SIAM Journal on Control and Optimization, 2007 - SIAM
In this paper we derive a posteriori error estimates for space-time finite element
discretizations of parabolic optimization problems. The provided error estimates assess the …

A priori error estimates for space-time finite element discretization of parabolic optimal control problems Part I: Problems without control constraints

D Meidner, B Vexler - SIAM Journal on Control and Optimization, 2008 - SIAM
In this paper we develop a priori error analysis for Galerkin finite element discretizations of
optimal control problems governed by linear parabolic equations. The space discretization …

A priori error estimates for space-time finite element discretization of parabolic optimal control problems part II: problems with control constraints

D Meidner, B Vexler - SIAM Journal on Control and Optimization, 2008 - SIAM
This paper is the second part of our work on a priori error analysis for finite element
discretizations of parabolic optimal control problems. In the first part [SIAM J. Control Optim …

Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations

E Casas, JP Raymond - SIAM Journal on Control and Optimization, 2006 - SIAM
We study the numerical approximation of boundary optimal control problems governed by
semilinear elliptic partial differential equations with pointwise constraints on the control. The …

Optimal control of the convection-diffusion equation using stabilized finite element methods

R Becker, B Vexler - Numerische Mathematik, 2007 - Springer
In this paper we analyze the discretization of optimal control problems governed by
convection-diffusion equations which are subject to pointwise control constraints. We …

Convergence and regularization results for optimal control problems with sparsity functional

G Wachsmuth, D Wachsmuth - ESAIM: Control, Optimisation and …, 2011 - cambridge.org
Optimization problems with convex but non-smooth cost functional subject to an elliptic
partial differential equation are considered. The non-smoothness arises from a L1-norm in …

Error estimates for the numerical approximation of boundary semilinear elliptic control problems

E Casas, M Mateos, F Tröltzsch - Computational Optimization and …, 2005 - Springer
We study the numerical approximation of boundary optimal control problems governed by
semilinear elliptic partial differential equations with pointwise constraints on the control. The …