Nonlinear complementarity problem: Difference between revisions

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{{Short description|Mathematics problem}}

{{Underlinked|date=February 2017}}

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

In [[applied mathematics]], a '''nonlinear complementarity problem (NCP)''' with respect to a mapping ''&fnof;''&nbsp;:&nbsp;'''R'''^''n''&nbsp;&rarr;&nbsp;'''R'''^''n'', denoted by NCP''&fnof;'', is to find a vector ''x''&nbsp;&isin;&nbsp;'''R'''^''n'' such that

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

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

where ''&fnof;''(''x'') is a smooth mapping.

== 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 |MRmr=1150683}}

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

* {{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}}

{{Mathematical programming}}

[[Category:MathematicalApplied optimizationmathematics]]