Invalid argument to QuadExpr multiplication for product of more than 2 variables

Awaiting user input

Cindy Li

• March 04, 2024 21:45
• Edited

Hi, I am trying to optimize the following:

Objective:
$$ \text{minimize} \quad ||B - PC||_1 $$

Here, matrix \(B\) is known, matrix \(P\) is entirely unknown, and matrix \(C\) is only partially known. The dimensions of both matrix \(P\) and \(C\) are known. \(||\cdot||_1\) denotes the \(L^1\) norm, which is the sum of the absolute values of the elements of the matrix \(B - PC\). 

 

However, it appears that QuadExpr does not support absolute values.

 

I have also tried changing the objective function to the following:

$$ \text{minimize} \quad ||B - PC||^2_F $$

But because some of the elements in matrix \(B - PC\) already contain products of two variables, getting its \(L^2\) norm results in the product of 4 variables, which I saw from other posts is not supported in gurobi.

 

I would appreciate any suggestions on how to circumvent the limitations! 

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  Gurobot (AI-generated response)

  Gurobi Staff

  • March 04, 2024 22:39

  To optimize an objective function involving the 1-norm (sum of absolute values) of a matrix in Gurobi, you can linearize the absolute values. For each element aijaij​ of your matrix, introduce two non-negative variables uijuij​ and vijvij​, and set aij=uij−vijaij​=uij​−vij​ and ∣aij∣=uij+vij∣aij​∣=uij​+vij​. Add constraints to ensure uij≥0uij​≥0 and vij≥0vij​≥0. This approach converts the absolute values into a linear form, which Gurobi can handle.

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