Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Analysis-Seminar Augsburg-München

 

Professor Dr. Constantin Christof
Universität Augsburg

 
spricht am
 
Donnerstag, 27. Oktober 2022
 
um
 
15:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Semismoothness for Solution Operators of Obstacle-type Variational Inequalities with Applications in Optimal Control«

Abstract:
This talk is concerned with generalized differentiability properties of solution operators of elliptic obstacle-type variational inequalities. We prove that such operators are semismooth when considered as maps between suitable Lebesgue spaces and equipped with the strong-weak Bouligand differential as a generalized set-valued derivative. It is shown that this semismoothness allows to solve optimal control problems with H1-cost terms and one-sided pointwise control constraints by means of a semismooth Newton method. The q-superlinear convergence of the resulting algorithm is established in the infinite-dimensional setting and its mesh independence is demonstrated in numerical experiments. The talk concludes with comments on further applications of the derived results in the context of quasi-variational inequalities and the optimal control of contact problems.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Malte Peter



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