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An extension of the projected gradient method to a Banach space setting with application in structural topology optimization

Blank, Luise and Rupprecht, Christoph (2015) An extension of the projected gradient method to a Banach space setting with application in structural topology optimization. Preprintreihe der Fakultät Mathematik 04/2015, Working Paper.

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Abstract

For the minimization of a nonlinear cost functional j under convex constraints the relaxed projected gradient process φk+1=φk+αk(PH(φk−λk∇Hj(φk))−φk) is a well known method. The analysis is classically performed in a Hilbert space H. We generalize this method to functionals j which are differentiable in a Banach space. Thus it is possible to perform e.g. an L2 gradient method if j is only ...

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Item type:Monograph (Working Paper)
Series of the University of Regensburg:Preprintreihe der Fakultät Mathematik
Date:2015
Institutions:Mathematics > Prof. Dr. Harald Garcke
Identification Number:
ValueType
1503.03783arXiv ID
Keywords:projected gradient method, variable metric method, convex constraints, shape and topology optimization, phase field approach
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Unknown
Refereed:No, this version has not been refereed yet (as with preprints)
Created at the University of Regensburg:Yes
Item ID:33149
Owner only: item control page

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