Trying to solve Sudoku with cvxpy
This is an ECOS_BB problem which you are using by default. It is not a reliable integer programming solver and I suggest not to use it.
Other recommendation: do not use import *
. It is much better to use import cvxpy as cp
to avoid confusion with other functions with the same name. Also, numpy is not needed here by the way.
The following script returns a feasible solution with GUROBI (you can also use GLPK if you do not have a GUROBI license):
import cvxpy as cp
x = cp.Variable((9, 9), integer=True)
# whatever, if the constrains are fulfilled it will be fine
objective = cp.Minimize(cp.sum(x))
constraints = [x >= 1, # all values should be >= 1
x <= 9, # all values should be <= 9
cp.sum(x, axis=0) == 45, # sum of all rows should be 45
cp.sum(x, axis=1) == 45, # sum of all cols should be 45
# sum of all squares should be 45
cp.sum(x[0:3, 0:3]) == 45, cp.sum(x[0:3, 3:6]) == 45,
cp.sum(x[0:3, 6:9]) == 45,
cp.sum(x[3:6, 0:3]) == 45, cp.sum(x[3:6, 3:6]) == 45,
cp.sum(x[3:6, 6:9]) == 45,
cp.sum(x[6:9, 0:3]) == 45, cp.sum(x[6:9, 3:6]) == 45,
cp.sum(x[6:9, 6:9]) == 45,
x[0, 7] == 7, # the values themselves
x[0, 8] == 1,
x[1, 1] == 6,
x[1, 4] == 3,
x[2, 4] == 2,
x[3, 0] == 7,
x[3, 4] == 6,
x[3, 6] == 3,
x[4, 0] == 4,
x[4, 6] == 2,
x[5, 0] == 1,
x[5, 3] == 4,
x[6, 3] == 7,
x[6, 5] == 5,
x[6, 7] == 8,
x[7, 1] == 2,
x[8, 3] == 1]
prob = cp.Problem(objective, constraints)
prob.solve(solver=cp.GUROBI)
print(x.value)
That's the output
In [2]: run sudoku.py
[[1. 6. 1. 4. 7. 9. 9. 7. 1.]
[6. 6. 1. 1. 3. 9. 9. 9. 1.]
[8. 7. 9. 1. 2. 9. 1. 7. 1.]
[7. 7. 1. 9. 6. 1. 3. 2. 9.]
[4. 9. 5. 9. 5. 1. 2. 1. 9.]
[1. 2. 9. 4. 9. 1. 9. 1. 9.]
[8. 1. 1. 7. 8. 5. 2. 8. 5.]
[9. 2. 9. 9. 4. 1. 1. 1. 9.]
[1. 5. 9. 1. 1. 9. 9. 9. 1.]]