Affine Transformation for objective function

回答済み

Gerardo Flores

2021年09月13日 18:32 編集済み

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My goal is to minimize the norm between the solution and a given matrix, I figured the best way to express it is via np.linalg.norm(x - ref_matrix). Essentially I want the solution matrix to deviate the least possible from a given matrix.

However, the command x - ref_matrix is not valid and I don't know how to implement such logic

ref_matrix = np.random.rand(79,682)
m = gp.Model()
x = m.addMVar(ref_matrix.shape, lb=0.0, ub=1.0)

for i in range(x.shape[0]):
   m.addConstr(x[i, :].sum() <= 1, name='date' + str(i))

m.setObjective(np.linalg.norm(x - ref_matrix), sense=gp.GRB.MINIMIZE)
m.optimize()

 

This will yield the following error:

 

gurobipy.GurobiError: Variable is not a 1D MVar object

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 02:47 編集済み

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
• 

  Eli Towle

  • Gurobi Staff

  2021年09月15日 01:28 編集済み

  You can introduce auxiliary variables \( Y \) equal to the difference between \( X \) and the reference matrix \( A \), then minimize \( ||Y||_F^2 \) by slicing the \( Y \) variables appropriately. For example:

  import gurobipy as gp
  from gurobipy import GRB
  import numpy as np
  
  n1 = 79
  n2 = 682
  A = np.random.rand(n1, n2)
  
  m = gp.Model()
  
  X = m.addMVar(shape=(n1, n2), ub=1.0, name='X')
  Y = m.addMVar(shape=(n1, n2), lb=-GRB.INFINITY, name='Y')
  
  # set Y = A - X
  m.addConstrs((Y[i, :] == X[i, :] - A[i, :] for i in range(n1)), name='set_Y')
  
  # "date" constraints
  m.addConstrs((X[i, :].sum() <= 1 for i in range(n1)), name='date')
  
  # minimize ||Y||_F^2
  m.setObjective(sum(Y[i, :] @ Y[i, :] for i in range(n1)), GRB.MINIMIZE)
  
  m.optimize()

  Minimizing \( ||Y||_F^2 \) is equivalent to minimizing \( ||Y||_F \).

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