Nonlinear complementarity problem

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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.

References

Stephen C. Billups (2008). A new homotopy method for solving non-linear complementarity problems. http://www.informaworld.com/smpp/content~db=all~content=a905306577. Retrieved 2010-03-13.
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

v · d · e Complementarity problems and algorithms

Complementarity Problems	Linear programming (LP) · Quadratic programming (QP) · Linear complementarity problem (LCP) · Mixed linear (MLCP) · Mixed (MCP) · Nonlinear(NCP)

Basis-exchange algorithms	Simplex (Dantzig) · Criss-cross · Lemke

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Nonlinear complementarity problem