[Python] What could I be doing wrong in this gurobi optimization problem, I have included the...

from gurobipy import Model, GRB, quicksum

I = 8 # Generators
J = 5 # Consumers
Gamma_q = 0 # Demand uncertainty budget
Delta_p = 0.5 # Capacity uncertainty budget
F = [53] * 2 + [30] * 6 # Fixed costs
C = [3] * 2 + [2] * 6 # Dispatch costs
p_max = [16] * 2 + [7] * 6 # Generator capacities
q = [8, 8, 3, 5, 16] # Consumer demands
total_demand = sum(q) # Total demand
# e_i = (0,…,0,1,0,…,0) ← 1 in the i‑th position only
e = {i: [1.0 if k == i else 0.0 for k in range(I)] for i in range(I)}
model = Model("ARO_Primal")

x = model.addVars(I, vtype=GRB.BINARY, name="x") # Commitment
u = model.addVars(I, vtype=GRB.CONTINUOUS, name="u") # Dispatch
V = model.addVars(I, J, vtype=GRB.CONTINUOUS, name="V") # Uncertainty variable for each (i, j)
eta = model.addVar(vtype=GRB.CONTINUOUS, name="eta") # Slack variable
t = model.addVars(J, vtype=GRB.CONTINUOUS, name="t") # Bounds for infinity norm terms
t_v = model.addVars(J,vtype=GRB.CONTINUOUS, name="t_v") # Infinity norm of 1-V
v_inf = model.addVars(I,J, vtype=GRB.CONTINUOUS, name="v_inf") # Infinity norm of V for (i, j)
t_inf = model.addVar(vtype=GRB.CONTINUOUS, name="t_inf") # Infinity norm of V
tv_inf = model.addVar(vtype=GRB.CONTINUOUS, name="tv_inf") # Infinity norm of V
v_new_inf = model.addVars(I,vtype=GRB.CONTINUOUS, name="v_new_inf") # Infinity norm of v_inf

Z = model.addVars(I, I, vtype=GRB.CONTINUOUS, name="Z")
Tz = model.addVars(I, vtype=GRB.CONTINUOUS, name="Tz") # ∑ C_i·Z[i,k]
tz_norm = model.addVar( vtype=GRB.CONTINUOUS, name="tz_norm") # ∥Tz∥∞
S = model.addVars(I, vtype=GRB.CONTINUOUS, name="S") # ∑ Z[i,k]
s_norm = model.addVar( vtype=GRB.CONTINUOUS, name="s_norm") # ∥S∥∞
z_inf = model.addVars(I, I, vtype=GRB.CONTINUOUS, name="z_inf") # ∥Z[i,k]∥∞ coords
z_new_inf = model.addVars(I, vtype=GRB.CONTINUOUS, name="z_new_inf")# ∥z_inf[i,·]∥∞
zdiff_inf = model.addVars(I, I, vtype=GRB.CONTINUOUS, name="zdiff_inf")# ∥Z[i,k]-x_i e_i[k]∥∞ coords
zdiff_norm= model.addVars(I, vtype=GRB.CONTINUOUS, name="zdiff_norm")# ∥zdiff_inf[i,·]∥∞

# Objective Function
model.setObjective(
quicksum(F * x for i in range(I)) + eta,
GRB.MINIMIZE
)

# Infinity norms for robust uncertainty (across all consumers `j`)
for j in range(J):
model.addConstr(t[j] >= quicksum(C * V[i, j] for i in range(I)), name=f"InfinityNorm_Pos_{j}") # Positive part
model.addConstr(t[j] >= -quicksum(C * V[i, j] for i in range(I)), name=f"InfinityNorm_Neg_{j}") # Negative part
# Infinity norms for robust uncertainty (across all consumers `j`)
for k in range(I):
model.addConstr(Tz[k] >= quicksum(C * Z[i, k] for i in range(I)), name=f"InfinityNorm_Postz_{k}") # Positive part
model.addConstr(Tz[k] >= -quicksum(C * Z[i, k] for i in range(I)), name=f"InfinityNorm_Negtz_{k}") # Negative part
for j in range(J):
model.addConstr(t_v[j] >= 1 - quicksum(V[i, j] for i in range(I)), name=f"InfinityNorm_Pos_t_v{j}")
model.addConstr(t_v[j] >= -1 + quicksum(V[i, j] for i in range(I)), name=f"InfinityNorm_Neg_t_v{j}")
for k in range(I):
model.addConstr(S[k] >= quicksum(Z[i,k] for i in range(I)), name=f"InfinityNorm_Pos_sk_{k}")
model.addConstr(S[k] >= -quicksum(Z[i,k] for i in range(I)), name=f"InfinityNorm_Neg_sk_{k}")
for k in range(I):
model.addConstr(tz_norm >= Tz[k], name=f"tzinf_pos_{k}")
model.addConstr(tz_norm >= -Tz[k], name=f"tzinf_neg_{k}")
for k in range(I):
model.addConstr(s_norm >= S[k], name=f"sinf_pos_{k}")
model.addConstr(s_norm >= -S[k], name=f"sinf_neg_{k}")

for i in range(I):
# z_inf coords
for k in range(I):
model.addConstr(z_inf[i,k] >= Z[i,k], name=f"zinf_pos_{i}_{k}")
model.addConstr(z_inf[i,k] >= -Z[i,k], name=f"zinf_neg_{i}_{k}")
for i in range(I):
for k in range(I):
expr = x*e[k] - Z[i,k]
model.addConstr(zdiff_inf[i,k] >= expr,
name=f"zdiff_pos_{i}_{k}")
model.addConstr(zdiff_inf[i,k] >= -expr,
name=f"zdiff_neg_{i}_{k}")

# Total Cost with Robust Uncertainty
for i in range(I):
for j in range(J):
model.addConstr(v_inf[i, j] >= V[i, j], name=f"InfinityNorm_Pos_v_{i}_{j}") # Positive part
model.addConstr(v_inf[i, j] >= -V[i, j], name=f"InfinityNorm_Neg_v_{i}_{j}") # Negative part


for j in range(J):
model.addConstr(t_inf >= t[j], name=f"InfinityNorm_t_inf_Pos_{j}")
model.addConstr(t_inf >= -t[j], name=f"InfinityNorm_t_inf_Neg_{j}") # Negative part

for j in range(J):
model.addConstr(tv_inf >= t_v[j], name=f"InfinityNorm_tv_inf_Pos_{j}")
model.addConstr(tv_inf >= -t_v[j], name=f"InfinityNormtv_inf_Neg_{j}") # Negative part
for i in range(I):
for j in range(J):
model.addConstr(v_new_inf >= v_inf[i, j], name=f"InfinityNorm_tv--_inf_Pos_{i}")
model.addConstr(v_new_inf >= -v_inf[i, j], name=f"InfinityNormtv--_Neg_{i}") # Negative part
for i in range(I):

for k in range(I):
model.addConstr(z_new_inf >= z_inf[i,k], name=f"znewinfpl_{i}_{k}")
model.addConstr(z_new_inf >= -z_inf[i,k], name=f"znewinf_{i}_{k}")

for i in range(I):

for k in range(I):
model.addConstr(zdiff_norm >= zdiff_inf[i,k], name=f"zdnormpl_{i}_{k}")
model.addConstr(zdiff_norm >= -zdiff_inf[i,k], name=f"zdnorm_{i}_{k}")
model.addConstr(
quicksum(C * u for i in range(I)) + Gamma_q * t_inf+Delta_p*tz_norm
<= eta,
name="TotalCostWithNorms"
)

model.addConstr(
quicksum(u for i in range(I)) == total_demand,
name="DemandSatisfaction"
)
# model.addConstr(u[1] >= u[0]+6.5, name="Distinguish_u1_u2")

# Capacity Constraints
for i in range(I):
model.addConstr(
u + Gamma_q * v_new_inf+Delta_p*zdiff_norm<= p_max[i] * x[i],
name=f"CapacityConstraint_{i}"
)
model.addConstr(
-u[i] + Gamma_q * v_new_inf[i]+Delta_p*z_new_inf[i] <= 0,
name=f"DispatchBound_{i}"
)

model.addConstr(
Gamma_q * tv_inf+Delta_p*s_norm <= 0,
name="UncertaintyBudget_V"
)


# Solve the model
model.optimize()

model.write("aro_debug.lp")

if model.status == GRB.OPTIMAL:
print("Optimal Cost:", model.objVal)
print("\nCommitments and Dispatch:")
for i in range(I):
print(f"∥Z[{i}]∥∞ = {z_new_inf[i].X}, ∥x_i e_i - Z[{i}]∥∞ = {zdiff_norm[i].X}")

for i in range(I):
print(f"Generator {i + 1}: x = {x[i].X}, u = {u[i].X}")
print("\nUncertainty Allocation (V):")
for i in range(I):
for j in range(J):
print(f"V[{i + 1}, {j + 1}] = {V[i, j].X}")
for i in range(I):
for k in range(I):
print(Z[i,k])
print(zdiff_inf[i,k])
print(zdiff_norm[i])
print(f"Z[{i},{k}]={Z[i,k].X:.2f}")
expected_Z = [
[ 5.75, 4.75, 5.75, -5.75, -5.75, -5.75, 5.75, -5.75],
[-5.75, -4.75, -5.75, 5.75, 5.75, 5.75, -5.75, 5.75],
[ 0.0, -0.5, 0.5, -0.5, 0.0, 0.5, 0.0, 0.5],
[ 0.5, 0.0, 0.0, 0.5, 0.5, 0.0, 0.5, -0.5],
[-0.5, -0.5, -0.5, 0.0, 0.5, -0.5, -0.5, 0.5],
[-0.5, 0.5, 0.5, -0.5, -0.5, 0.5, -0.5, -0.5],
[ 0.5, 0.5, -0.5, 0.5, -0.5, -0.5, 0.5, 0.0],
[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
]
for i in range(I):
actual = [Z[i,k].X for k in range(I)]
print(i, actual, "matches?", all(abs(actual[k] - expected_Z[i][k])<1e-6 for k in range(I)))

expected_V = [
[0.25625, 0.25625, 0.25625, 0.25625, 0.25625],
[0.25625, 0.25625, 0.25625, 0.25625, 0.25625],
[0.16250, 0.16250, 0.16250, 0.16250, 0.16250],
[0.16250, 0.16250, 0.16250, 0.16250, 0.16250],
[0.00000, 0.00000, 0.00000, 0.00000, 0.00000],
[0.00000, 0.00000, 0.00000, 0.00000, 0.00000],
[0.16250, 0.16250, 0.16250, 0.16250, 0.16250],
[0.00000, 0.00000, 0.00000, 0.00000, 0.00000],
]

print("\nChecking V against expected_V:")
for i in range(I):
actual_row = [V[i, j].X for j in range(J)]
match = all(abs(actual_row[j] - expected_V[i][j]) < 1e-6
for j in range(J))
print(f"Row {i}: {actual_row} matches? {match}")

[LIST=1]
[*]could you see what is wrong with my code since I am trying to have the function below into my gurobi code what should I do what is wrong with my code I'm trying to verify the solution of a robust optimization model that involves matrix variables [B]Z[/B] and [B]V[/B], where [B]Z[/B] represents the perturbations to the identity matrix and [B]V[/B] is derived from it under specific norm constraints. Specifically, I'm modeling ∞-norm constraints on the rows of [B]Z[/B] and their deviation from a scaled identity matrix to ensure robustness in the objective. I'm using Gurobi in Python to formulate and solve the model, and I'm hardcoding expected values of [B]Z[/B] and [B]V[/B] to validate that the optimization behaves as intended. However, despite building the model correctly in parts, my constraints aren't fully enforced due to miswritten or missing loops, leading to incorrect or zero solutions for [B]Z[/B] and [B]V[/B]. I’ve also realized that some constraints like the infinity-norm budget or the deviation bounds weren’t actually connected to the model as I intended. I haven’t tried alternative formulations yet (like dualizing or simplifying the problem), but I’m currently focused on correctly enforcing the ∞-norm constraints element-wise to reproduce the desired matrix values. I'm looking for feedback on both my formulation strategy and implementation pitfalls—especially how to make sure these types of norm-bounded constraints are applied properly in a solver like Gurobi.
[/LIST]


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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<title>Styled Optimization Model</title>

<!-- MathJax v3 -->
<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>

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<div class="math-block">
\[
\begin{aligned}
\min_{x,u,V,Z,\eta}\;& \sum_{i=1}^I F_i x_i + \eta \\[4pt]
\mathrm{s.t.}\;&
\sum_{i=1}^I C_i u_i
+ \Gamma_q \Big\|\sum_{i=1}^I C_i V_i\Big\|_{\ell_*}
+ \Delta_p \Big\|\sum_{i=1}^I C_i Z_i\Big\|_{\ell_*}
\;\le\;\eta, \\[6pt]
&\Gamma_q \Big\|1 - \sum_{i=1}^I V_i\Big\|_{\ell_*}
+ \Delta_p \Big\|-\sum_{i=1}^I Z_i\Big\|_{\ell_*}
\;\le\;0, \\[6pt]
&\sum_{i=1}^I u_i \;=\;\sum_{j=1}^J \bar q_j, \\[6pt]
&u_i
+ \Gamma_q \|V_i\|_{\ell_*}
+ \Delta_p \|\,x_i e_i - Z_i\|_{\ell_*}
\;\le\;p_i^{\max}x_i,
\quad\forall i, \\[6pt]
&-\,u_i
+ \Gamma_q \|V_i\|_{\ell_*}
+ \Delta_p \|Z_i\|_{\ell_*}
\;\le\;0,
\quad\forall i, \\[6pt]
&x_i \in\{0,1\},
\quad\forall i.
\end{aligned}
\]
</div>

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