geometric programming with mosek

[Thomas Pumir]

Hi all,

Forgive the naivety of the question but I'm a new Mosek user here. 

I'm looking at  the following (geometric, integer) problem below:

\begin{align*}
\min_x & \sum_i \frac{\beta_i}{x_i} \\
& \sum_i x_i \leq K \\
& 1 \leq x_i \leq \alpha_i \\
& x_i \in \mathbb{N}
\end{align*}

Would anyone be kind enough to point me to the formulation of the objective function using the MOSEK Python API (I got the rest of the variables/constraints right) 

Assuming I'm not mistaken it should be something of the like: 

 M.objective('obj', ObjectiveSense.Minimize, Expr.dot(beta,1/x)) 

Thank you very much for your attention/help!!

Best,