Convergence of Non-smooth Descent Methods Using the Kurdyka–Łojasiewicz Inequality

Dominikus Noll ()
Additional contact information
Dominikus Noll: Université Paul Sabatier

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 2, No 10, 553-572

Abstract: Abstract We investigate the convergence of subgradient-oriented descent methods in non-smooth non-convex optimization. We prove convergence in the sense of subsequences for functions with a strict standard model, and we show that convergence to a single critical point may be guaranteed if the Kurdyka–Łojasiewicz inequality is satisfied. We show, by way of an example, that the Kurdyka–Łojasiewicz inequality alone is not sufficient to prove the convergence to critical points.

Keywords: Non-smooth non-convex optimization; Subgradient-oriented descent method; Strict model; Kurdyka–Łojasiewicz inequality; Upper- and lower-C 1 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0391-8 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:160:y:2014:i:2:d:10.1007_s10957-013-0391-8

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

DOI: 10.1007/s10957-013-0391-8

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 ().