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Abstract
We consider a non‐smooth convex variational problem appearing as a formal limit of compliance minimization in the vanishing volume ratio limit. The problem has a classical basis pursuit form, and several successful algorithms have been utilized to solve problems of this class in other application contexts. We discuss the well‐posedness and regularity of solutions to these problems, possible solution algorithms, and their discretizations as relevant in this mechanical engineering context. We then test the algorithms on a few benchmark problems with available analytical solutions.
We find that whereas many algorithms are successful in estimating the optimal objective value to the problem to a high accuracy, the same cannot be said about finding the optimal solutions themselves. In particular, in some examples the algorithms struggle to properly identify the areas where the solutions should vanish entirely. We also discuss an example where the found optimal solutions are not sparse even though sparse(r) solutions exist.
We find that whereas many algorithms are successful in estimating the optimal objective value to the problem to a high accuracy, the same cannot be said about finding the optimal solutions themselves. In particular, in some examples the algorithms struggle to properly identify the areas where the solutions should vanish entirely. We also discuss an example where the found optimal solutions are not sparse even though sparse(r) solutions exist.
Original language  English 

Article number  e202000008 
Journal  Zeitschrift fuer Angewandte Mathematik und Mechanik 
Volume  100 
Issue number  9 
Number of pages  19 
ISSN  00442267 
DOIs  
Publication status  Published  2020 
Keywords
 Compliance minimization
 Convex optimization
 Nonsmooth optimization
 Splitting algorithms
 Sparse solutions
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Dive into the research topics of 'Sparse basis pursuit for compliance minimization in the vanishing volume ratio limit'. Together they form a unique fingerprint.Projects
 1 Active

InnoTop: InnoTop, Interactive, NonLinear, HighResolution Topology Optimization
Sigmund, O., Carlberg, L. K., Aage, N., Andreasen, C. S., Wang, F., Bærentzen, J. A. & Miladinovic, K. S.
01/09/2017 → 31/08/2023
Project: Research