Optimality conditions for a multiobjective bilevel optimization problem involving set valued constraints

ABSTRACT

In this paper, we investigate a multiobjectif bilevel programming problem with set valued constraints in both the upper problem and the lower problem. Using the notion of the support function to the feasible set mapping, together with an appropriate constraint qualification, we establish necessary optimality conditions in terms of asymptotical pointwise compact approximations; continuity of data functions and compactness of approximations are not necessarily required. In order to get sufficient optimality conditions, we introduce generalized pseudo-invexity and quasi-invexity notions in terms of asymptotical pointwise compact approximations. Examples that illustrate our results are given.

KEYWORDS:

• Approximations
• multiobjective optimization
• optimality conditions
• support functions
• bilevel programming

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C26
• 90C29
• 90C30
• 90C46
• 49K99

Disclosure statement

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