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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 (2017) An Extension of the Projected Gradient Method to a Banach Space Setting with Application in Structural Topology Optimization. SIAM Journal on Control and Optimization 55 (3), pp. 1481-1499.

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Other URL: http://doi.org/10.1137/16M1092301


Abstract

For the minimization of a nonlinear cost functional under convex constraints the relaxed projected gradient process is a well known method. The analysis is classically performed in a Hilbert space. We generalize this method to functionals which are differentiable in a Banach space. The search direction is calculated by a quadratic approximation of the cost functional using the idea of the ...

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Item type:Article
Date:2017
Institutions:Mathematics > Prof. Dr. Luise Blank
Identification Number:
ValueType
10.1137/16M1092301DOI
Keywords:PHASE FIELD MODEL; CONVERGENCE; ALGORITHMS; DESIGN; projected gradient method; variable metric method; convex constraints; shape and topology optimization; phase field approach
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:38839
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