Necessary optimality conditions for a bilevel multiobjective programming problem via a Ψ-reformulation

ABSTRACT

In this paper, we are concerned with a bilevel multiobjective optimization problem . First, using Ψ, a function introduced by Gadhi and Dempe [Necessary optimality conditions and a new approach tomulti-objective bilevel optimization problems. J Optim Theory Appl. 2012;155:100–114], we transform into a one level optimization problem . Second, on terms of convexificators, using a scalarization technique, we derive a Karash-Kuhn-Tucker (KKT)-type necessary optimality conditions to the initial problem under a generalized Abadie constraint qualification without the assumption that the lower-level problem satisfies the Mangasarian Fromovitz constraint qualification. Some examples have been introduced to illustrate our results.

KEYWORDS:

• Multiobjective optimization
• local weak efficient solution
• optimality conditions
• Ψ-function
• bilevel programming

AMS SUBJECT CLASSIFICATIONS:

• 90C26
• 90C29
• 90C30
• 90K46

Disclosure statement

No potential conflict of interest was reported by the authors.