Establishing explicit formulas of coderivatives with respect to a set of the normal cone mapping to a polyhedron, the solution set of a variational inequality system, is one of the main goals of this paper. By using our coderivative formulas, we provide a characteristic of the Aubin property with respect to a set of that normal cone mapping and then give necessary optimality conditions for simple bilevel optimization problems under weak qualification conditions.
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Thinh et al. (2026) studied this question.
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