Nonlinear complementarity problem

In applied mathematics, a nonlinear complementarity problem (NCP) with respect to a mapping &fnof; : Rn &rarr; Rn, denoted by NCP&fnof;, is to find a vector x &isin; Rn such that


 * $$x \geq 0,\ f(x) \geq 0 \text{ and } x^{T}f(x)=0 $$

where &fnof;(x) is a smooth mapping. The case of a discontinuous mapping was discussed by Habetler and Kostreva (1978).