Norm 1 of a MVar as Constraint
AnsweredHello. I am trying to add a Constraint to my Matrix oriented program that checks if the norm 1 of the matrix variable is less than a p parameter. (With norm 1 beign the sum of the absolute values of each position of the MVar). I've been trying to use abs_() but then the GenExpr form makes it impossible to sum or iterate.
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Gurobi Staff
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Hello José, unfortunately there isn't a shorthand for doing this in gurobipy yet, but I have taken note of your feature request in our development backlog.
For now you will have to model the absolute values per variable. For example, to compute a minimum 1-norm solution to an underdetermined linear system you could do:
import numpy as np
import gurobipy as gp
A = np.random.rand(30, 100)
x_true = np.random.rand(100)
b = A @ x_true
m = gp.Model()
x = m.addMVar(100, lb=-np.inf)
m.addConstr(A @ x == b)
# 'absx' takes absolute value of 'x'
absx = m.addMVar(100)
for v, absv in zip(x.tolist(), absx.tolist()):
m.addConstr(absv == gp.abs_(v))
# minimize 1-norm of x
m.setObjective(absx.sum())
m.optimize()
print("Solution 1-norm: {}".format(np.sum(np.abs(x.X))))0 -
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Thank you so much Robert!
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Hi José,
Gurobi 9.5 was recently released. Included in this release is the norm() general constraint helper function that can be used to set a decision variable equal to the norm of the other decision variables. The supported norms are 0-, 1-, 2-, and infinity.
We hope this new feature works well for you. Please let us know if you find any issues using this.
Best regards,
Maliheh
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