Titelaufnahme

Titel
PDE-constrained optimization subject to pointwise control and zero- or first-order state constraints
VerfasserHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Kunisch, Karl In der Gemeinsamen Normdatei der DNB nachschlagen
Erschienen in
SIAM Journal on Optimization, Philadelphia, Pa., 2009, Jg. 20, H. 3, S. 1133-1156
ErschienenSIAM
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)constraint qualification / gradient constraints / first-order optimality system / lifting, MoreauYosida regularization / PDE-constrained optimization / pointwise state constraints / semi-smooth Newton method
ISSN1095-7189
URNurn:nbn:at:at-ubg:3-1015 Persistent Identifier (URN)
DOIdoi:10.1137/080737265 
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PDE-constrained optimization subject to pointwise control and zero- or first-order state constraints [4.9 mb]
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Zusammenfassung (Englisch)

A general MoreauYosida-based framework for minimization problems subject to partial differential equations and pointwise constraints on the control, the state, and its derivative is considered. A range space constraint qualification is used to argue existence of Lagrange multipliers and to derive a KKT-type system for characterizing first-order optimality of the unregularized problem. The theoretical framework is then used to develop a semismooth Newton algorithm in function space and to prove its locally superlinear convergence when solving the regularized problems. Further, for maintaining the local superlinear convergence in function space it is demonstrated that in some cases it might be necessary to add a lifting step to the Newton framework in order to bridge an L2-Lr-norm gap, with r > 2. The paper ends by a report on numerical tests.

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