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The Global ETD Search service is a free service for researchers
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Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Showing 1 to 8 of 8 (0.022 seconds)Spelling suggestions: "subject:"MSC 49220"" "subject:"MSC 49020""
| 1 |
Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic EquationsMalanowski, Kazimierz, Tröltzsch, Fredi 30 October 1998 (has links) (PDF)
A class of parametric optimal control problems for semilinear parabolic
equations is considered. Using recent regularity results for solutions of such equations,
sufficient conditions are derived under which the solutions to optimal control problems
are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown
that these conditions are also necessary, provided that the dependence of data on the
parameter is sufficiently strong.
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| 2 |
Second Order Sufficient Optimality Conditions for Nonlinear Parabolic Control Problems with State ConstraintsRaymond, Jean-Pierre, Tröltzsch, Fredi 30 October 1998 (has links) (PDF)
In this paper, optimal control problems for semilinear parabolic equations with
distributed and boundary controls are considered. Pointwise constraints on the control and on
the state are given. Main emphasis is laid on the discussion of second order sufficient optimality
conditions. Sufficiency for local optimality is verified under different assumptions imposed
on the dimension of the domain and on the smoothness of the given data.
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| 3 |
Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbationsTröltzsch, F. 30 October 1998 (has links) (PDF)
We consider a class of control problems governed by a linear parabolic initial-boundary
value problem with linear-quadratic objective and pointwise constraints on the control.
The control system contains different types of perturbations. They appear in the
linear part of the objective functional, in the right hand side of the equation,
in its boundary condition, and in the initial value. Making use of parabolic regularity
in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm
is improved to the supremum-norm.
|
| 4 |
Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic EquationsMalanowski, Kazimierz, Tröltzsch, Fredi 30 October 1998 (has links)
A class of parametric optimal control problems for semilinear parabolic
equations is considered. Using recent regularity results for solutions of such equations,
sufficient conditions are derived under which the solutions to optimal control problems
are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown
that these conditions are also necessary, provided that the dependence of data on the
parameter is sufficiently strong.
|
| 5 |
On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic EquationsTröltzsch, Fredi 30 October 1998 (has links) (PDF)
A class of Lagrange-Newton-SQP methods is investigated for optimal control problems
governed by semilinear parabolic initial- boundary value problems. Distributed and boundary
controls are given, restricted by pointwise upper and lower bounds. The convergence of the method
is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition
for the reference solution, local quadratic convergence is proved. The proof is based on the
theory of Newton methods for generalized equations in Banach spaces.
|
| 6 |
Second Order Sufficient Optimality Conditions for Nonlinear Parabolic Control Problems with State ConstraintsRaymond, Jean-Pierre, Tröltzsch, Fredi 30 October 1998 (has links)
In this paper, optimal control problems for semilinear parabolic equations with
distributed and boundary controls are considered. Pointwise constraints on the control and on
the state are given. Main emphasis is laid on the discussion of second order sufficient optimality
conditions. Sufficiency for local optimality is verified under different assumptions imposed
on the dimension of the domain and on the smoothness of the given data.
|
| 7 |
Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbationsTröltzsch, F. 30 October 1998 (has links)
We consider a class of control problems governed by a linear parabolic initial-boundary
value problem with linear-quadratic objective and pointwise constraints on the control.
The control system contains different types of perturbations. They appear in the
linear part of the objective functional, in the right hand side of the equation,
in its boundary condition, and in the initial value. Making use of parabolic regularity
in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm
is improved to the supremum-norm.
|
| 8 |
On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic EquationsTröltzsch, Fredi 30 October 1998 (has links)
A class of Lagrange-Newton-SQP methods is investigated for optimal control problems
governed by semilinear parabolic initial- boundary value problems. Distributed and boundary
controls are given, restricted by pointwise upper and lower bounds. The convergence of the method
is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition
for the reference solution, local quadratic convergence is proved. The proof is based on the
theory of Newton methods for generalized equations in Banach spaces.
|
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