Moreau–Rockafellar Theorems for Nonconvex Set-Valued Maps

P. H. Sach ()
Additional contact information
P. H. Sach: Institute of Mathematics

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 2, No 6, 213-227

Abstract: Abstract In this paper, we introduce the notion of (Benson) proper subgradient of a set-valued map and prove that, for some class of nonconvex set-valued maps, a proper subgradient of the sum of two set-valued maps can be expressed as the sum of two proper subgradients of these maps. This property is also established for weak subgradients. A result in Ref. [Lin, L.J.: J. Math. Anal. Appl. 186, 30–51 (1994)], obtained under some convexity assumption, is included as a special case of the corresponding result of this paper.

Keywords: Moreau–Rockafellar theorem; Benson proper subgradients; Set-valued maps; Generalized convexity (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-007-9173-5 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:133:y:2007:i:2:d:10.1007_s10957-007-9173-5

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

DOI: 10.1007/s10957-007-9173-5

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 ().