Nonlinear complementarity problem

Short description: Mathematics 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

[math]\displaystyle{ x \geq 0,\ f(x) \geq 0 \text{ and } x^{T}f(x)=0 }[/math]

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. (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. 
• 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.