How to linearize a constraint that containing square of sum of product?

Question

I am working on an optimization problem. In order to solve it using CPLEX, we need to linearize the non-linear constraint stated in the following.

$$\left(\sum_{i,j \in A}\mu _{i,j}X_{i,j,t}\right) ^2 \ge \sum_{i,j \in A}\sigma_{i,j}^2X_{i,j,t}$$

Where $X_{i,j,t}$ is binary variable and all remain ones are parameters.

Answer 1

One approach is to expand the square and linearize each resulting product of binary variables in the usual way.

Alternatively, just use the MIQCP solver in CPLEX.