Second-Order Strong Karush/Kuhn–Tucker Conditions for Proper Efficiencies in Multiobjective Optimization

Min Feng () and Shengjie Li ()
Additional contact information
Min Feng: Chongqing University
Shengjie Li: Chongqing University

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 5, 766-786

Abstract: Abstract In this paper, strong Karush/Kuhn–Tucker conditions are studied for smooth multiobjective optimization with inequality constraints. We introduce a new second-order regularity condition of Abadie type in terms of the second-order directional derivatives and then obtain a second-order strong Karush/Kuhn–Tucker necessary condition at a Borwein-properly efficient solution. Simultaneously, we also use an example to show that, if the Abadie type regularity condition is weakened to the Guignard type one, the second-order strong Karush/Kuhn–Tucker necessary condition may not hold. Finally, then we also apply the second-order strong Karush/Kuhn–Tucker conditions to derive a sufficient result for local Geoffrion-proper efficiency.

Keywords: Multiobjective optimization; Strong Karush/Kuhn–Tucker conditions; Second-order regularity conditions; Second-order optimality conditions; Borwein-properly efficient solutions; Geoffrion-proper efficiency; 26A24; 49K99; 90C29 (search for similar items in EconPapers)
Date: 2019
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/s10957-019-01484-0 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:181:y:2019:i:3:d:10.1007_s10957-019-01484-0

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

DOI: 10.1007/s10957-019-01484-0

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 ().