I have two functions $f(x,y)$ and $g(x,y)$ whose sum/product (whichever is possible) is to be minimized. The values of $x,y$ can vary in the interval $0<x,y<1$ (hence none of them can have a value of $1$ or $0$). The range of function $f(x,y)$ is from $0$ to $1$ while function $g(x,y)$ can have any value in the real set.
For function of two variables I know one technique called the Biconvex optimization. I can apply this technique if both of the functions are Biconvex however one of my function is Biconvex (namely $g(x,y)$) while the other is not Biconvex hence I can not apply this technique here. Are there other techniques which I can use for these types of optimization problems? Any suggestions will be highly appreciated.
Thanks in advance.
Edit: After reading this post (Optimization of a function of two variables.) I am quite confused about my statement of Biconvex optimization please shed some light over it also.