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. 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 t 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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