In applied mathematics, a nonlinear complementarity problem (NCP) with respect to a mapping ƒ : R<sup>n</sup> → R<sup>n</sup>, denoted by NCPƒ, is to find a vector x ∈ R<sup>n</sup> such that
where ƒ(x) is a smooth mapping. The case of a discontinuous mapping was discussed by Habetler and Kostreva (1978).