Approximate Karush–Kuhn–Tucker Condition in Multiobjective Optimization

Giorgio Giorgi (), Bienvenido Jiménez () and Vicente Novo ()
Additional contact information
Giorgio Giorgi: University of Pavia
Bienvenido Jiménez: Universidad Nacional de Educación a Distancia (UNED)
Vicente Novo: Universidad Nacional de Educación a Distancia (UNED)

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 1, No 4, 70-89

Abstract: Abstract We extend the so-called approximate Karush–Kuhn–Tucker condition from a scalar optimization problem with equality and inequality constraints to a multiobjective optimization problem. We prove that this condition is necessary for a point to be a local weak efficient solution without any constraint qualification, and is also sufficient under convexity assumptions. We also state that an enhanced Fritz John-type condition is also necessary for local weak efficiency, and under the additional quasi-normality constraint qualification becomes an enhanced Karush–Kuhn–Tucker condition. Finally, we study some relations between these concepts and the notion of bounded approximate Karush–Kuhn–Tucker condition, which is introduced in this paper.

Keywords: Approximate optimality conditions; Sequential optimality conditions; Enhanced Fritz John conditions; Enhanced Karush–Kuhn–Tucker conditions; Vector optimization problems; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-0986-y 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:171:y:2016:i:1:d:10.1007_s10957-016-0986-y

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

DOI: 10.1007/s10957-016-0986-y

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 ().