# Pseudo-monotone function

$LaTeX: \textstyle f: \mathbb{R}^n \to \mathbb{R}^n$ is pseudo-monotone over $LaTeX: X$ (subset of $LaTeX: \textstyle \mathbb{R}^n$) if
$LaTeX: f(y)^T (x - y) \ge 0 \mbox{ implies } f(x)^T (x - y) \ge 0 \mbox{ for all } x, y \in X.$