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

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

• Ahuja, Kapil; Watson, Layne T.; Billups, Stephen C. (December 2008). "Probability-one homotopy maps for mixed complementarity problems". Computational Optimization and Applications. 41 (3): 363–375. doi:10.1007/s10589-007-9107-z. hdl:10919/31539 .
• 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.

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