# How can I deal with a possibly undefined constraint?

I have a minimization problem minimizing $$d_k \geq 0$$ and some other variables with all strictly positive coefficients. I leave my objective function below to better convey my goal.

$$\min_{\mathbf{d},\mathbf{y^+},\mathbf{y^-}} \sum_{k\in\mathcal{K}} C_k d_k +\sum_{(i,j)\in\mathcal{E},k\in\mathcal{K}}P\lambda_kT_{ij}\left(y_{ijk}^+ +y_{ijk}^-\right)$$

To determine the value of $$d_k$$, I have the following constraint which can possibly become undefined due to the domains of variables associated. Simply, if all $$y^+$$ and $$y^-$$ variables are 0...

$$d_k \geq \frac{\displaystyle\sum_{i\in \mathcal{I}_k}\lambda_k y_{ikk}^+}{\displaystyle\sum_{(i,j)\in\mathcal{E}} T_{ij}\left(y_{ijk}^+ +y_{ijk}^-\right)}\qquad \forall k\in \mathcal{K}$$

Notation Domains:

$$\begin{array}{c|c|c} & \text{Domain} & \text{Type}\\ \hline d_k & \mathbb{R}^{\geq0} & \text{Variable} \\ \hline y_{ijk}^+ & \{0,1\} & \text{Variable} \\ \hline y_{ijk}^- & \{0,1\} & \text{Variable} \\ \hline \lambda_k & \mathbb{R}^{>0} & \text{Parameter} \\ \hline T_{ij} & \mathbb{R}^{>0}& \text{Parameter} \\ \hline C_k & \mathbb{R}^{>0}& \text{Parameter} \\ \hline P & \mathbb{R}^{>0}& \text{Parameter} \\ \end{array}$$

Sets:

The sets: $$\mathcal{I}$$, $$\mathcal{K}$$, $$\mathcal{E}$$ are some polynomial size sets and $$\mathcal{I}_k$$ is a subset.

Is there a way to deal with nonlinearity and "0/0"?

Multiply both sides of your $$d_k \ge$$ constraint by the denominator and then linearize $$d_k y_{ijk}^+$$ and $$d_k y_{ijk}^-$$ as described in this thread.