Faces and Support Functions for the Values of Maximal Monotone Operators

Bao Tran Nguyen () and Pham Duy Khanh ()
Additional contact information
Bao Tran Nguyen: Universidad de O’Higgins
Pham Duy Khanh: HCMC University of Education

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 6, 843-863

Abstract: Abstract Representation formulas for faces and support functions of the values of maximal monotone operators are established in two cases: either the operators are defined on reflexive and locally uniformly convex real Banach spaces with locally uniformly convex duals, or their domains have nonempty interiors on real Banach spaces. Faces and support functions are characterized by the limit values of the minimal-norm selections of maximal monotone operators in the first case while in the second case they are represented by the limit values of any selection of maximal monotone operators. These obtained formulas are applied to study the structure of maximal monotone operators: the local unique determination from their minimal-norm selections, the local and global decompositions, and the unique determination on dense subsets of their domains.

Keywords: Maximal monotone operator; Face; Support function; Minimal-norm selection; Yosida approximation; Strong convergence; Weak convergence; 26B25; 47B48; 47H04; 47H05; 54C60 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-020-01737-3 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:186:y:2020:i:3:d:10.1007_s10957-020-01737-3

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

DOI: 10.1007/s10957-020-01737-3

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 ().