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How do I multiply an array and a 2-D MVar object using the matrix-friendly Python API?

Eli Towle
  • Updated

Operations with 2-D MVar objects are largely unsupported. For example, let \( a \in \mathbb{R}^m \), let \(b \in \mathbb{R}^n \), and let \(X\) be an \( m \times n \) MVar object. Attempting to construct the expression \( a^\top X b \) with the following code results in GurobiError: Variable is not a 1D MVar object:

import gurobipy as gp
import numpy as np

model = gp.Model()
X = model.addMVar((3,4))

a = np.random.rand(3)
b = np.random.rand(4)

model.setObjective(a @ X @ b)  # error!

Currently, matrix linear expressions can only be constructed from 1-D MVar objects. Instead, the expression \( a^\top X b \) can be built by appropriately slicing the 2-D \( X \) matrix variable:

import gurobipy as gp
import numpy as np

model = gp.Model()
X = model.addMVar((3,4))

a = np.random.rand(3)
b = np.random.rand(4)

model.setObjective(sum(b[j] * a @ X[:, j] for j in range(4)))

Note: Gurobi 9.0 introduced the first version of the Python matrix API. The developers are continually working to improve the usability of the matrix API.

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