Optimality conditions in terms of convexificators for a bilevel multiobjective optimization problem

ABSTRACT

In this paper, we are concerned with a multiobjective bilevel optimization problem $\left(P\right)$, where the lower-level problem is also a multiobjective optimization problem. Using the optimal-value reformulation, together with a scalarization technique, under a nonsmooth generalized Guignard constraint qualification, one gives necessary optimality conditions for the initial problem. As an application, one deduces optimality conditions for a scalar bilevel programming problem in terms of convexificators. An example is given to illustrate our findings.

KEYWORDS:

• Bilevel optimization
• guignard constraint qualification
• convexificators
• optimal value function
• optimality conditions

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 90C29
• 90C26
• 90C70
• Secondary 49K99

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the author(s).