Nonlinear complementarity problem explained

In applied mathematics, a nonlinear complementarity problem (NCP) with respect to a mapping ƒ : Rⁿ → Rⁿ, denoted by NCPƒ, is to find a vector x ∈ Rⁿ such that

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

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

References

• Ahuja . Kapil . Watson . Layne T. . Billups . Stephen C. . Probability-one homotopy maps for mixed complementarity problems . Computational Optimization and Applications . December 2008 . 41 . 3 . 363–375 . 10.1007/s10589-007-9107-z. 10919/31539 . free .
• Book: Cottle. Richard W.. Pang. Jong-Shi. Stone. Richard E.. The linear complementarity problem . Computer Science and Scientific Computing. Academic Press, Inc.. Boston, MA. 1992. xxiv+762 pp. 0-12-192350-9 . 1150683.