Generalized equation

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This has the form: 0 is in LaTeX: \{f(x)\} + T(x), where LaTeX: f is a function from LaTeX: \mathbb{R}^n into LaTeX: \mathbb{R}^n and LaTeX: T is a point to set map that maps LaTeX: x into subsets of LaTeX: \mathbb{R}^n. If LaTeX: T is absent, the condition reduces to an ordinary equation, LaTeX: f(x)=0. Usually, LaTeX: T is assumed to satisfy the monotonicity condition:

LaTeX: 
(x-x')^T(y-y') \ge 0 \mbox{ for } y \in T(x) \mbox{ and } y' \in T(x').

This includes a variational inequality (and hence the complementarity problem) as a special case.


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