Abstract
ABSTRACT In this paper, we are concerned with a semivectorial bilevel optimization problem 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.
Published Version
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