Paper Info
Title
Shape Optimization with Nonsmooth Cost Functions: From Theory to Numerics.
Abstract
This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semiderivative of the cost function by employing the averaged adjoint approach and maximal elliptic regularity. Furthermore we characterize stationary points and show how to compute steepest descent directions theoretically and practically. Finally, we present some numerical results for a simple toy problem and compare them with the smooth case. We observe faster convergence rates in the nonsmooth case in our tests.
Year
DOI
Venue
2016
10.1137/16M1069882
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
shape optimization,nonsmooth cost functions,PDE constraints
Convergence (routing),Discrete mathematics,Mathematical optimization,Gradient descent,Toy problem,Mathematical analysis,Eulerian path,Stationary point,Lipschitz continuity,Mathematics
Journal
Volume
Issue
ISSN
54
6
0363-0129
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Kevin Sturm121.12