Nonlinear complementarity problem: Difference between revisions

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{{Short description|Mathematics problem}}

==Definition==

In [[applied mathematics]], a '''nonlinear complementarity problem''' ('''NCP''') with respect to a mapping ''ƒ'' : '''R'''^''n'' → '''R'''^''n'', denoted by NCP''ƒ'', is to find a vector ''x'' ∈ '''R'''^''n'' such that

: <math>x \geq 0,\ f(x) \geq 0 </math>\text{ and <math>} x^{T}f(x)=0 </math>

A '''Nonlinear Complementarity Problem (NCP)''' with respect to a mapping <math>f: \mathbb{R}^n \to \mathbb{R}^n</math>, denoted by NCP<math>(f)</math>, is to find a vector <math>x \in \mathbb{R}^n</math> such that

: <math>x \geq 0, f(x)\geq 0 </math> and <math> x^{T}f(x)=0</math>

where <math>f''&fnof;''(''x'')</math> is a smooth mapping. The case of a discontinuous mapping was discussed by Habetler and Kostreva (1978).

== References ==

* {{cite paperjournal |last1=Ahuja |first1=Kapil |last2=Watson |first2=Layne T. |last3=Billups |authorfirst3=Stephen C. Billups|title=A newProbability-one homotopy methodmaps for solving non-linearmixed complementarity problems |journal=Computational Optimization and Applications |date=December 2008 |volume=41 |issue=3 |pages=363–375 |doi=10.1007/s10589-007-9107-z|hdl=10919/31539 |hdl-access=free }}

* {{cite book|last1=Cottle|first1=Richard W.|last2=Pang|first2=Jong-Shi|last3=Stone|first3=Richard E.|title=The linear complementarity problem | series=Computer Science and Scientific Computing|publisher=Academic Press, Inc.|___location=Boston, MA|year=1992|pages=xxiv+762 pp|isbn=0-12-192350-9 |mr=1150683}}

url=http://www.informaworld.com/smpp/content~db=all~content=a905306577|accessdate=2010-03-13}}

{{Mathematical programming}}

[[Category:MathematicalApplied optimizationmathematics]]

{{applied-math-stub}}