I have formulated the following problem:
\begin{align} \max \quad & e^{- \boldsymbol \alpha^T \boldsymbol x/N} \\ \text{s.t.} \quad & \boldsymbol1^T\boldsymbol x = N \\ & \boldsymbol x \geqslant \boldsymbol 0 \\ & \boldsymbol 0 \leqslant \boldsymbol \alpha \leqslant \boldsymbol 1 \end{align}
Here, $\boldsymbol x$ and $\boldsymbol \alpha$ are vectors; $N$ is a scalar. $N$ is given, $\boldsymbol \alpha$ is a variable, and the optimisation variable is $\boldsymbol x$.
The objective function needs to be maximised for each $x_i$ in vector $\boldsymbol x$. But, the objective function is non-convex. How do I transform it into a convex form? Or else, how do I solve it otherwise?