On a Monotone Scheme for Nonconvex Nonsmooth Optimization with Applications to Fracture Mechanics

Daria Ghilli () and Karl Kunisch ()
Additional contact information
Daria Ghilli: Karl-Franzens University
Karl Kunisch: Karl-Franzens University

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 2, No 11, 609-641

Abstract: Abstract A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition of a regularized version of the original problem is solved by means of a monotonically convergent scheme. Such problems arise in continuum mechanics, as for instance cohesive fractures, where singular behaviour is usually modelled by nonsmooth nonconvex energies. The proposed algorithm is successfully tested for fracture mechanics problems. Its performance is also compared to two alternative algorithms for nonsmooth nonconvex optimization arising in optimal control and mathematical imaging.

Keywords: Nonsmooth nonconvex optimization; Monotone algorithm; Fracture mechanics; Sparse recovery; 49M05; 49Kxx; 65Kxx; 74Rxx; 74Pxx; 49J53; 49K99 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01545-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:183:y:2019:i:2:d:10.1007_s10957-019-01545-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01545-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().