The problem of the number of switches in parabolic equations with control
Andrzej Karafiat (1977)
Annales Polonici Mathematici
Similarity:
Andrzej Karafiat (1977)
Annales Polonici Mathematici
Similarity:
Ira Neitzel, Fredi Tröltzsch (2008)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated...
E. Fabes, N. Garofalo, S. Salsa (1990)
Colloquium Mathematicae
Similarity:
M. Farag (1997)
Applicationes Mathematicae
Similarity:
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
S. Farag, M. Farag (2000)
Applicationes Mathematicae
Similarity:
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
Hongwei Lou (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.
Maïtine Bergounioux, Fredi Tröltzsch (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear...
Ira Neitzel, Fredi Tröltzsch (2009)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated...
M. Bergounioux, F. Troeltzsch (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of control theory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-state inequality constraints. We show how to obtain Lagrange multipliers in L spaces for linear problems and give an application to linear parabolic optimal control problems.