First-order optimality conditions in set-valued optimization

Giovanni Crespi (), Ivan Ginchev () and Matteo Rocca ()

Mathematical Methods of Operations Research, 2006, vol. 63, issue 1, 87-106

Abstract: A a set-valued optimization problem min C F(x), x ∈X 0 , is considered, where X 0 ⊂ X, X and Y are normed spaces, F: X 0 ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x 0 ,y 0 ), y 0 ∈F(x 0 ), and are called minimizers. The notions of w-minimizers (weakly efficient points), p-minimizers (properly efficient points) and i-minimizers (isolated minimizers) are introduced and characterized through the so called oriented distance. The relation between p-minimizers and i-minimizers under Lipschitz type conditions is investigated. The main purpose of the paper is to derive in terms of the Dini directional derivative first order necessary conditions and sufficient conditions a pair (x 0 , y 0 ) to be a w-minimizer, and similarly to be a i-minimizer. The i-minimizers seem to be a new concept in set-valued optimization. For the case of w-minimizers some comparison with existing results is done. Copyright Springer-Verlag 2006

Keywords: Vector optimization; Set-valued optimization; First-order optimality conditions; 90C29; 90C30; 90C46; 49J52 (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-005-0023-7 (text/html)
Access to full text is restricted to subscribers.

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:63:y:2006:i:1:p:87-106

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

DOI: 10.1007/s00186-005-0023-7

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 ().