Necessary optimality conditions for a semivectorial bilevel problem under a partial calmness condition

ABSTRACT

In this paper, we are concerned with a semivectorial bilevel optimization problem $\left(P\right).$ Using a partial calmness suitable for bilevel semivectorial problems, we formulate its necessary optimality conditions. Our approach consists of reformulating our problem into a one level optimization problem using successively the kth-objective weighted-constraint and the optimal value reformulation. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions are then derived in the smooth setting while using the generalized differentiation calculus of Mordukhovich.

KEYWORDS:

• Partial calmness
• limiting subdifferential
• limiting normal cone
• optimality condition
• semivectorial bilevel program

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 90C29
• 90C26
• 90C46
• Secondary 49K99

Disclosure statement

No potential conflict of interest was reported by the authors.