My problem is: \begin{align}\min\limits_{x_{ij}}\qquad&{\sum_{i\in N}\sum_{j\in M}\frac{x_{ij}}{C_j-\sum\limits_{i\in N} x_{ij}a_i}}\\\text{s.t.}\qquad&0<C_j-\sum_{i\in N} x_{ij}a_i\\\qquad&\sum_{j\in M} x_{ij}=1\\\qquad&x_{ij}\in[0,1]\\\quad&{\sum_{j\in M}\frac{x_{ij}}{C_j-\sum\limits_{i\in N} x_{ij}a_i}} \le d_i,\forall i\in N\end{align}
It is worth mentioning that the third constraint indicates the range and $x_{ij}$ isn't binary. As I calculated the Hessian of my objective function, I understood that the sign of matrix elements is dependent on $x_{ij}$ and $C_j-\sum\limits_{i\in N} x_{ij}a_i$ which are always positive or zero.
- Due to this, can I conclude that my problem is convex?
- If the answer is yes, what class of convex problems does it belong to? (conic, geometric, etc.) and if no what is the type of problem?