Consider a corecive function $h$ on $\mathbb{R}^n$ and a minimization problem on $h$: Minimize $h(x)$, with $x\in \{(x_1,x_2\ldots,x_n):x_i\in\{-1,0,1\}\}$.
How can we determine the number of local but not global minimizers of the function $h$? There exists a global minimimum by virtue of coercivity in $\mathbb{R}^n$. But, does there exist a minimum in the above domain? How should we proceed? Thanks beforehand.