On Lagrange Multiplier Rules for Set-Valued Optimization Problems in the Sense of Set Criterion. (25th April 2020)

• Record Type: Journal Article
• Authors: Amahroq, Tijani; Oussarhan, Abdessamad; Syam, Aicha
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 6(2020)
• Page Start: 710
• Page End: 729
• Publication Date: 2020-04-25
• Subjects: Fritz John multipliers -- Karush-Kuhn-Tucker multipliers -- optimality conditions -- oriented distance function -- set-valued optimization; 54C60 -- 90C29 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1667828
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we obtain a new scalar representation of set-valued optimization problems by using a criterion of solution introduced by Kuroiwa, this criterion is a weaker version of Pareto efficient solution. Following this scalarization, we establish necessary optimality conditions in terms of Fritz John multipliers as well as Karush-Kuhn-Tucker multipliers. Moreover, we give sufficient optimality conditions.