I am working on a large-scale Mixed Integer Linear Programming (MILP) problem using Gurobi. The decision variable vector x is binary and has a dimension of approximately n = 40,000,000. The objective function is defined as:

obj = c * x

where c is a coefficient vector of the same size as x.

I also need to add a very large number of constraints in batch form. Specifically, the constraints are of the form:

A * x <= b

where:

A is a matrix with dimensions n x n_col, where n_col is approximately 3,000,000.

B is a vector of size n.

Given the scale of the problem, I need to avoid adding constraints iteratively and instead handle them in a batched manner. I am looking for the most efficient way to add these constraints to the Gurobi model.

My questions are:

• Is it possible to add constraints like A * x <= B in a single batch using Gurobi’s API?

• What is the most efficient way to handle this size of constraints in Gurobi?

• Are there any performance tips or methods (e.g., using sparse matrices) to manage this large-scale problem effectively?