Solution to Optimisation problem

Hello

I have a simple optimization problem that includes a 2-norm constraint on a vector. When I read the .lp problem below and solve it with gurobi, then I get the answer that some norm variables take the value 1.0, when the 2-norm of the vector [0,0,0,0,0,1,-1,0] should be sqrt(2).

However, if I add a lower bound to the norm variables, such as (lb = -100) (which wouldn't make much sense), then it gives me the correct norm, i.e. sqrt(2). The lower bound I added with:
```

norm[intersection_1_1] >= -100
norm[intersection_1_2] >= -100
norm[intersection_2_1] >= -100
```

And the solution I get is
```

Best objective 2.000000000000e+00, best bound 2.000000000000e+00, gap 0.0000%
norm[intersection_1_1] 1.0
norm[intersection_1_2] 1.0
norm[intersection_2_1] 0.0
z[0] -0.0
z[1] -0.0
z[2] -0.0
z[3] -0.0
z[4] -0.0
z[5] 0.0
z[6] 1.0
z[7] 0.0
diff[intersection_1_1,0] 0.0
diff[intersection_1_1,1] 0.0
diff[intersection_1_1,2] 0.0
diff[intersection_1_1,3] 0.0
diff[intersection_1_1,4] 0.0
diff[intersection_1_1,5] 1.0
diff[intersection_1_1,6] -1.0
diff[intersection_1_1,7] 0.0
diff[intersection_1_2,0] 0.0
diff[intersection_1_2,1] 0.0
diff[intersection_1_2,2] 0.0
diff[intersection_1_2,3] 0.0
diff[intersection_1_2,4] 0.0
diff[intersection_1_2,5] 0.0
diff[intersection_1_2,6] -1.0
diff[intersection_1_2,7] 1.0
diff[intersection_2_1,0] 0.0
diff[intersection_2_1,1] 0.0
diff[intersection_2_1,2] 0.0
diff[intersection_2_1,3] 0.0
diff[intersection_2_1,4] 0.0
diff[intersection_2_1,5] 0.0
diff[intersection_2_1,6] 0.0
diff[intersection_2_1,7] 0.0

```

I don't know where the issue is and would appreciate any help to solve it. Thanks
```

Minimize
[ 2 norm[intersection_1_1] ^2 + 2 norm[intersection_1_2] ^2
+ 2 norm[intersection_2_1] ^2 ] / 2
Subject To
z_constr: z[0] + z[1] + z[2] + z[3] + z[4] + z[5] + z[6] + z[7] = 1
diff_intersection_1_1[0]: z[0] + diff[intersection_1_1,0] = 0
diff_intersection_1_1[1]: z[1] + diff[intersection_1_1,1] = 0
diff_intersection_1_1[2]: z[2] + diff[intersection_1_1,2] = 0
diff_intersection_1_1[3]: z[3] + diff[intersection_1_1,3] = 0
diff_intersection_1_1[4]: z[4] + diff[intersection_1_1,4] = 0
diff_intersection_1_1[5]: z[5] + diff[intersection_1_1,5] = 1
diff_intersection_1_1[6]: z[6] + diff[intersection_1_1,6] = 0
diff_intersection_1_1[7]: z[7] + diff[intersection_1_1,7] = 0
diff_intersection_1_2[0]: z[0] + diff[intersection_1_2,0] = 0
diff_intersection_1_2[1]: z[1] + diff[intersection_1_2,1] = 0
diff_intersection_1_2[2]: z[2] + diff[intersection_1_2,2] = 0
diff_intersection_1_2[3]: z[3] + diff[intersection_1_2,3] = 0
diff_intersection_1_2[4]: z[4] + diff[intersection_1_2,4] = 0
diff_intersection_1_2[5]: z[5] + diff[intersection_1_2,5] = 0
diff_intersection_1_2[6]: z[6] + diff[intersection_1_2,6] = 0
diff_intersection_1_2[7]: z[7] + diff[intersection_1_2,7] = 1
diff_intersection_2_1[0]: z[0] + diff[intersection_2_1,0] = 0
diff_intersection_2_1[1]: z[1] + diff[intersection_2_1,1] = 0
diff_intersection_2_1[2]: z[2] + diff[intersection_2_1,2] = 0
diff_intersection_2_1[3]: z[3] + diff[intersection_2_1,3] = 0
diff_intersection_2_1[4]: z[4] + diff[intersection_2_1,4] = 0
diff_intersection_2_1[5]: z[5] + diff[intersection_2_1,5] = 0
diff_intersection_2_1[6]: z[6] + diff[intersection_2_1,6] = 1
diff_intersection_2_1[7]: z[7] + diff[intersection_2_1,7] = 0
Bounds
-2 <= diff[intersection_1_1,0] <= 2
-2 <= diff[intersection_1_2,0] <= 2
-2 <= diff[intersection_2_1,0] <= 2
-2 <= diff[intersection_1_1,1] <= 2
-2 <= diff[intersection_1_2,1] <= 2
-2 <= diff[intersection_2_1,1] <= 2
-2 <= diff[intersection_1_1,2] <= 2
-2 <= diff[intersection_1_2,2] <= 2
-2 <= diff[intersection_2_1,2] <= 2
-2 <= diff[intersection_1_1,3] <= 2
-2 <= diff[intersection_1_2,3] <= 2
-2 <= diff[intersection_2_1,3] <= 2
-2 <= diff[intersection_1_1,4] <= 2
-2 <= diff[intersection_1_2,4] <= 2
-2 <= diff[intersection_2_1,4] <= 2
-2 <= diff[intersection_1_1,5] <= 2
-2 <= diff[intersection_1_2,5] <= 2
-2 <= diff[intersection_2_1,5] <= 2
-2 <= diff[intersection_1_1,6] <= 2
-2 <= diff[intersection_1_2,6] <= 2
-2 <= diff[intersection_2_1,6] <= 2
-2 <= diff[intersection_1_1,7] <= 2
-2 <= diff[intersection_1_2,7] <= 2
-2 <= diff[intersection_2_1,7] <= 2
Binaries
z[0] z[1] z[2] z[3] z[4] z[5] z[6] z[7]
General Constraints
normconstr_intersection_1_1: norm[intersection_1_1] = NORM ( 2 ) (
diff[intersection_1_1,0] , diff[intersection_1_1,1] ,
diff[intersection_1_1,2] , diff[intersection_1_1,3] ,
diff[intersection_1_1,4] , diff[intersection_1_1,5] ,
diff[intersection_1_1,6] , diff[intersection_1_1,7] )
normconstr_intersection_1_2: norm[intersection_1_2] = NORM ( 2 ) (
diff[intersection_1_2,0] , diff[intersection_1_2,1] ,
diff[intersection_1_2,2] , diff[intersection_1_2,3] ,
diff[intersection_1_2,4] , diff[intersection_1_2,5] ,
diff[intersection_1_2,6] , diff[intersection_1_2,7] )
normconstr_intersection_2_1: norm[intersection_2_1] = NORM ( 2 ) (
diff[intersection_2_1,0] , diff[intersection_2_1,1] ,
diff[intersection_2_1,2] , diff[intersection_2_1,3] ,
diff[intersection_2_1,4] , diff[intersection_2_1,5] ,
diff[intersection_2_1,6] , diff[intersection_2_1,7] )
End
``

Official comment

Simranjit Kaur

Gurobi Staff

November 13, 2026 01:29

This post is more than two 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 try Gurobot, our chatbot interface offering instant, expert-level support.

Riley Clement

February 25, 2024 06:02

Hi Vinzenz,

I can't seem to reproduce your issue. Solving the LP file you posted, with Gurobi v11, the running:

for v in m.getVars():
    print(v.varname, v.X, v.lb)

I get the following output:

norm[intersection_1_1] 1.4142135623730931 0.0
norm[intersection_1_2] 0.0 0.0
norm[intersection_2_1] 1.4142135603441 0.0

Can you provide some more details on how you are running this (including Gurobi version)?

- Riley

Vinzenz Tütsch

February 25, 2024 10:14

Hi Riley,

Thanks for your answer. I'm using Gurobi 11.0.0.

I'll share some code, so you can see what I do exactly. It is not exactly the same problem, but a condensed version that gives me the same error:

import gurobipy as gp
from gurobipy import GRB
import numpy as np

env = gp.Env(empty=True)
env.setParam("OutputFlag", 0)
env.start()

# Create a new model
model = gp.Model("norm_objective_example", env=env)

x1 = np.array([0, 1, 0, 0, 0, 0, 0, 0])
x2 = np.array([0, 0, 1, 0, 0, 0, 0, 0])
n = len(x1)

# Define the variables
z = model.addVars(n, vtype=GRB.BINARY, name="z")
diff = model.addVars(2, n, vtype = GRB.CONTINUOUS, lb=-2, ub=2, name="diff")
norm = model.addVars(2, vtype = GRB.CONTINUOUS, name="norm")

# Add constraints
model.addConstr(z.sum() == 1)
for i in range(n):
    model.addConstr(diff[0, i] == x1[i] - z[i])
    model.addConstr(diff[1, i] == x2[i] - z[i])

# Add the norm constraint
model.addGenConstrNorm(norm[0], diff.select(0, "*"), 2.0, "normconstr0")
model.addGenConstrNorm(norm[1], diff.select(1, "*"), 2.0, "normconstr1")

# Set the objective
model.setObjective(norm[0] + norm[1], GRB.MINIMIZE)

# Optimize the model
model.optimize()

print("Z:", [z_val.X for z_val in z.select()])
print("Diff 1:", [dif.X for dif in diff.select(0, "*")])
print("Diff 2:", [dif.X for dif in diff.select(1, "*")])
print("Norm 0:", norm[0].X)
print("Norm 1:", norm[1].X)

Z: [-0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0]
Diff 1: [0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Diff 2: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Norm 0: 1.0
Norm 1: 0.0

February 25, 2024 10:56

Thanks for the simplified model, I can confirm I can replicate your results with v11.

I note that when output is turned on the log indicates there are issues with the solution:

Warning: max constraint violation (4.1421e-01) exceeds tolerance
Warning: max general constraint violation (4.1421e-01) exceeds tolerance
         (model may be infeasible or unbounded - try turning presolve off)

Setting Presolve=0 as suggested gives the expected answer. Additionally the mention of "infeasible or unbounded" immediately brings to mind dual reductions and setting DualReductions=0 also resolves the issue.

But this outcome is still not ideal, and there does not seem to be an issue with v10 so I will open a support request for this, as it will make it easier for us to look into this internally. You will receive a notification shortly.

February 25, 2024 12:31

Thanks for opening a request and your help.

Solution to Optimisation problem

Comments

Didn't find what you were looking for?