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Main Title: Sufficient second-order optimality conditions for convex control constraints
Author(s): Wachsmuth, Daniel
Type: Research Paper
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.
Subject(s): optimal control
sufficient second-order conditions
strongly active sets
convex control constraints
measurable set-valued functions
Navier-Stokes equations
Issue Date: 18-Oct-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 49K20 Problems involving partial differential equations
26E25 Set-valued functions
49J53 Set-valued and variational analysis
76D05 Navier-Stokes equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 30
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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