I have this optimization problem which is linear and therefore convex. how should I calculate the closed form solution:
$\min_{\eta_i} \max_i \frac{\eta_i+\beta_i}{R_i}$ s.t. $\sum \eta_i=\alpha$ and $\eta_i \geq 0$
where $\beta_i$'s and $R_i$'s are all positive.
so I wrote it as the linear form of
$\min_{\eta_i} K$ s.t. $K\geq \frac{\eta_i+\beta_i}{R_i}$ and $\eta_i \geq 0$
which indicates a linear programming. How should I find the closed form solution.