Can anyone please help me with solving the constrained minimization problem below?

$$\mathbf{x}^* = \arg\min \sum_{i=1}^m q_i e^{-2x_i} $$ $$s.t.$$ $$\sum_{i=1}^m x_i = c$$ $$x_i\geq0, i = 1,\cdots,m$$

where $\mathbf{x}=[x_1,\cdots,x_m]^T$ is the unknown vector and $\mathbf{q}=[q_1,\cdots,q_m]^T$ and $c$ are given constants.

Do I need to consider the KKT conditions for this?

Or, can this problem be solved as a linear program by considering the exponential part as a sort of kernel?