Inhalt des Dokuments
Preprint 30-2004
Sufficient second-order optimality conditions for convex control constraints
Author(s) :
Daniel Wachsmuth
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 30-2004
MSC 2000
- 49K20 Problems involving partial differential equations
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26E25 Set-valued functions
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49J53 Set-valued and variational analysis
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76D05 Navier-Stokes equations
Abstract :
In this article sufficient optimality conditions are established for optimal control problems
with pointwise convex control constraints. Here, the control is a function with values in Rn.
The constraint is of the form u(x) ∈ U(x), where U is an set-valued mapping that is assumed to
be measurable with convex and closed images.
The second-order condition requires
coercivity of the Lagrange function on a suitable subspace, which excludes strongly active constraints,
together with first-order necessary
conditions. It ensures local optimality of a reference function in a L∞-neighborhood.
The analysis is done for a model problem namely the optimal distributed control of the instationary Navier-Stokes equations.
Keywords :
Optimal control, sufficient second-order conditions, strongly active sets, convex control constraints, measurable set-valued functions, Navier-Stokes equations