# Biconvex function

A function $LaTeX: f(x, y)$ on $LaTeX: X \times Y$ that is convex on $LaTeX: X$ for each $LaTeX: y \in Y$ and convex on $LaTeX: Y$ for each $LaTeX: x \in X$. An example is $LaTeX: f(x,y) = xy$ on $LaTeX: \mathbb{R}^2$, which is not convex in both $LaTeX: x$ and $LaTeX: y$ together.