# Variational inequality

$LaTeX: \textstyle \mbox{Let F:X} \to \mathbb{R}^n.$ The variational inequality problem is to find $LaTeX: \textstyle x \in \mbox{X}$ such that $LaTeX: \textstyle \mbox{F}(x)(y-x) \ge 0 \mbox{ for all } y \in \mbox{X.}$ This includes the complementarity problem.