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

URN to cite this document:: urn:nbn:de:bvb:355-epub-331499
DOI to cite this document:: 10.5283/epub.33149

Blank, Luise ; Rupprecht, Christoph

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Date of publication of this fulltext: 12 Jan 2016 13:00

Alternative links to fulltext:Arxiv

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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 ...