How does a non-convex optimization problem can be solved to get a near optimal solution?

Question

I have an optimization problem of the form $f(x_1,x_2,y_1,y_2) = \frac{y_1}{x_1} + \frac{y_2}{x_2}$ for all real values of $x_1,x_2,y_1,y_2$ . Also $f$ is found to be non-convex in nature. I want to minimize this non-convex function $f$. How can I get a near optimal solution of this $f$?

Answer 1

The problem is unbounded.

Let $y_2=0$ $x_1=1$, and let $y_1 = k$, then $f(x_1,x_2,y_1,y_2)=k$ and $k$ can take arbitrary negative values.