Nonlinear complementarity problem: Difference between revisions

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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

==Definition==

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.

== References ==