I know the difference of two convex functions is called D.C. Program, see Horst R, Thoai N V. DC programming: overview[J]. Journal of Optimization Theory and Applications, 1999, 103(1): 1-43.
However, I am wondering what is the difference of two concave functions called? Is there any existing results for this problem? Specifically, I have $f(x) = g(x) - h(x): \mathbb{R}^d \rightarrow \mathbb{R}$, where $g(x)$ and $h(x)$ are concave functions. What will be the computational complexity if I want to minimize/maximize $f(x)$? Intuitively, it's NP-Hard because either maximizing a convex and minimizing a concave function is NP-Hard in general, is it true for $\underset{x}{\text{min/max }} f(x)$