I'm new in optimization and I have a problem involving minimizing the sum of two functions f(x) and g(x). The objective function must be in such a way that f(x) has to be minimized and g(x) maximized, besides g(x) has a constant $\beta$ that determines it's importance ($\beta \in [0,1]$)
I have read that one solution is an objective function like this
\begin{equation} f(x)- \beta g(x) \end{equation}
and also found that could be
\begin{equation} f(x)+ \frac{\beta}{g(x)} \end{equation}
But I'am not really sure. Could you please help me? or provide me some book or anything in order to understand more about the optimization involving this case.
Thank you.