Displaying similar documents to “Continuous Dependence Results for Subdifferential Inclusions”

Optimality conditions for semilinear parabolic equations with controls in leading term

Hongwei Lou (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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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.

On an optimal control problem for a quasilinear parabolic equation

S. Farag, M. Farag (2000)

Applicationes Mathematicae

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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.

Optimality conditions for semilinear parabolic equations with controls in leading term

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.

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel, Fredi Tröltzsch (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD

Eileen Kammann, Fredi Tröltzsch, Stefan Volkwein (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced...

The gradient projection method for solving an optimal control problem

M. Farag (1997)

Applicationes Mathematicae

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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.