Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization

L. Huerga (), B. Jiménez (), V. Novo () and A. Vílchez ()
Additional contact information
L. Huerga: E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Ciudad Universitaria
B. Jiménez: E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Ciudad Universitaria
V. Novo: E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Ciudad Universitaria
A. Vílchez: E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Ciudad Universitaria

Mathematical Methods of Operations Research, 2021, vol. 93, issue 2, No 7, 413-436

Abstract: Abstract In the setting of normed spaces ordered by a convex cone not necessarily solid, we use six set scalarization functions, which are extensions of the oriented distance of Hiriart-Urruty, and we discuss convexity and continuity properties of their composition with two set-valued maps. Furthermore, as an application, we derive a multiplier rule for weak minimal solutions of a convex set optimization problem, with respect to the lower set less preorder of Kuroiwa. Some illustrative examples are also given.

Keywords: Oriented distance; Set optimization; Set order relations; Scalarization in set optimization; Convexity; Continuity; Lagrange multipliers; 06A75; 49J53; 90C29 (search for similar items in EconPapers)
Date: 2021
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/s00186-020-00736-4 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:mathme:v:93:y:2021:i:2:d:10.1007_s00186-020-00736-4

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-020-00736-4

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().