Necessary and Sufficient Conditions for Robust Minimal Solutions in Uncertain Vector Optimization

Marcin Studniarski (), Anna Michalak () and Aleksandra Stasiak ()
Additional contact information
Marcin Studniarski: University of Łódź
Anna Michalak: University of Łódź
Aleksandra Stasiak: University of Łódź

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 2, No 2, 375-397

Abstract: Abstract We introduce a new notion of a vector-based robust minimal solution for a vector-valued uncertain optimization problem, which is defined by means of some open cone. We present necessary and sufficient conditions for this kind of solution, which are stated in terms of some directional derivatives of vector-valued functions. To prove these results, we apply the methods of set-valued analysis. We also study relations between our definition and three other known optimality concepts. Finally, for the case of scalar optimization, we present two general algorithm models for computing vector-based robust minimal solutions.

Keywords: Uncertain optimization; Robust minimal solutions; Set-valued analysis; Radial derivatives; 49J52; 49J53; 49N30; 90C31 (search for similar items in EconPapers)
Date: 2020
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/s10957-020-01714-w 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:2:d:10.1007_s10957-020-01714-w

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

DOI: 10.1007/s10957-020-01714-w

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 ().