I'm looking at the following (non-convex) quadratic program
$$\begin{array}{ll} \underset{x_1,\dots, x_n}{\text{minimize}} & a \displaystyle\sum_{i=1}^n x_i - b \displaystyle\sum_{i=1}^n x_i^2\\ \text{subject to} & \alpha_{\min} \leq \displaystyle\sum_{i=1}^n x_i \leq \alpha_{\max}\\ & \beta_{\min}\leq x_i \leq \beta_{\max}, \quad \forall i=1,\dots, n\end{array}$$
with $a, b, \alpha_{\min}, \alpha_{\max}, \beta_{\min}, \beta_{\max} > 0$.
I don't really know where to start. The first term (not squared) is minimized for low $x_i$ while the second part is minimized for high $x_i$.
Any suggestions?