How do I square a MVar matrix in the objective function?

Ongoing

Rachel Orsini

October 26, 2020 23:12

Hello,

I have several MVars in my model and I would like to square them in the objective function - is this possible? I have Python 3.7 and Gurobi 9.0.

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Official comment
Simranjit Kaur

Gurobi Staff

December 06, 2024 00:40
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Eli Towle

Gurobi Staff

October 28, 2020 02:38 Edited
Do you mean you want to take the sum of the squared vector values (i.e., \( ||x||_2^2\))? If your matrix is 1D, this is equal to the dot product of the vector with itself:
```
import gurobipy as gp

m = gp.Model()
x = m.addMVar(3, name='x')
m.setObjective(x @ x)
```
The above code adds the objective \( x_1^2 + x_2^2 + x_3^2 \).

If you have a 2D matrix of variables and you want to calculate the sum of the squared matrix values (\( ||X||_F^2\)), you can iterate over the rows (or columns) of the matrix, summing the squared L2 norms of each matrix slice:
```
import gurobipy as gp

m = gp.Model()
x = m.addMVar((3,3), name='x')
m.setObjective(sum(x[i, :] @ x[i, :] for i in range(3)))
```
This code adds the objective \( x_{11}^2 + x_{12}^2 + \ldots + x_{33}^2 \).
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