Multiobjective Problems: Enhanced Necessary Conditions and New Constraint Qualifications through Convexificators. (2nd January 2018)

• Record Type: Journal Article
• Authors: Alavi Hejazi, Mansoureh; Movahedian, Nooshin; Nobakhtian, Soghra
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 1(2018)
• Page Start: 11
• Page End: 37
• Publication Date: 2018-01-02
• Subjects: Constraint qualification -- convexificator -- multiobjective optimization problem -- necessary optimality condition -- nonsmooth analysis -- pseudo-differential; 49J52 -- 90C29 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1351455
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjective problems involving inequality and equality constraints in terms of convexificators. We develop the enhanced Karush–Kuhn–Tucker conditions and introduce the associated pseudonormality and quasinormality conditions. We also introduce several other new constraint qualifications which entirely depend on the feasible set. Then a connecting link between these constraint qualifications is presented. Moreover, we provide several examples that clarify the interrelations between the different results that we have established.