Nonlinear complementarity problem

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

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

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

References

• Stephen C. Billups (2008). "A new homotopy method for solving non-linear complementarity problems". {{cite journal}}: Cite journal requires |journal= (help)
• Cottle, Richard W.; Pang, Jong-Shi; Stone, Richard E. (1992). The linear complementarity problem. Computer Science and Scientific Computing. Boston, MA: Academic Press, Inc. pp. xxiv+762 pp. ISBN 0-12-192350-9. MR 1150683.