A function $f(x, y): B\to R$ is called a biconvex function if fixing $x$, $f_x(y)=f(x, y)$ is convex over $Y$ and fixing $y$, $f_y(x)=f(x, y)$ is convex over $X$. $B$ is a biconvex set that is, $B \subset X\times Y$ if for every fixed $y \in Y$, $B_y= \{x\in X: (x, y)\in B\}$ is a convex set in $X$ and for every fixed $x \in X$, $B_x= \{y\in Y: (x, y)\in B\}$ is a convex set in $Y$. I am trying to understand this class of functions, looking for interesting functions that fall in this category and Optimization methods.
My Understanding:
I know that convex function has this property that they are convex on all lines passing through the domain. We can tell similar things for Biconvex Functions, that they are convex on all lines parallel to Axes and passing through the domain.
From the above definition, we can construct functions which have many local minima along lines not parallel to Axes. In such a scenario is it even possible to reach a global minima? If yes can you please give an intuitive idea to do that?