Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a Ψ reformulation

ABSTRACT

In this paper, we are concerned with a bilevel multiobjective optimization problem $\left(P\right)$. Using the function Ψ introduced by Gadhi and Dempe [Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems. J Optim Theory Appl. 2012;155:100–114], we reformulate $\left(P\right)$ as a single level mathematical programming problem $\left(P^{\ast }\right)$ and establish/exhibit the global equivalence between the two problems $\left(P\right)$ and $\left(P^{\ast }\right)$. Using a generalized convexity introduced by Dutta and Chandra [Convexificator, generalized convexity and vector optimization. Optimization. 2004;53:77–94], we derive sufficient optimality conditions for the problem $\left(P\right)$ and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.

KEYWORDS:

• Bilevel programming
• convexificator
• duality
• efficient solution
• Ψ-function

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 90C29
• 90C46
• Secondary 49K99

Acknowledgements

Our sincere acknowledgements to the anonymous referees for their insightful remarks and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the Alexander-von Humboldt Foundation.