cyipopt gives weird solution on simple optimization problem?

[GuanJinNL]

Dear Ipopt community,

I have recently started using ipopt through python and I conda installed the cyipopt package as well as the ipopt solver through conda forge.

I copy-pasted the example code on cyipopt documentation page and it worked fine. However, when I tried a simple optimization problem, the solver gives weird solution.
The simple problem that I tried was: minimize x[0] + x[1], subject to x[0]-x[1]<= 0, x[0]>=0.
Obviously, the solution to this problem should be 0.

I defined the problem in the same way as suggested on the cyipopt page:

class HS073(cyipopt.Problem):

def objective(self, x):
    """Returns the scalar value of the objective given x."""
     return(x[0]+x[1])

def gradient(self, x):
    """Returns the gradient of the objective with respect to x."""
    return(np.array([1,1]))
   
def constraints(self, x):
    """Returns the constraints."""
    return(np.array([x[0]-x[1]]))

def jacobian(self, x):
    """Returns the Jacobian of the constraints with respect to x."""
    return(np.array([1,-1]))


def intermediate(self, alg_mod, iter_count, obj_value, inf_pr, inf_du, mu,
                 d_norm, regularization_size, alpha_du, alpha_pr,
                 ls_trials):
    """Prints information at every Ipopt iteration."""
    iterate = self.get_current_iterate()
    infeas = self.get_current_violations()
    primal = iterate["x"]
    jac = self.jacobian(primal)
    msg = "Objective value at iteration #{:d} is - {:g}"

    print(msg.format(iter_count, obj_value))

    print("Iteration:", iter_count)
    print("Primal iterate:", primal)
    print("Flattened Jacobian:", jac)
    print("Dual infeasibility:", infeas["grad_lag_x"])

Then, I added the bounds and formulate the problem:

lb = [0,0]
ub = [2e10,2e10]
cl = [-2e10]
cu = [0]
x0 = [1,2]

nlp = HS073(
n=len(x0),
m=len(cl),
lb=lb,
ub=ub,
cl=cl,
cu=cu,
)

Finally, I solve the problem:

nlp.add_option('mu_strategy', 'adaptive')
nlp.add_option('tol', 1e-10)
x, info = nlp.solve(x0)

This is the output. After 1 iteration, the solution is not making sense:

Objective value at iteration #0 is - 3
Iteration: 0
Primal iterate: [1. 2.]
Flattened Jacobian: [ 1 -1]
Dual infeasibility: [1. 1.]
Objective value at iteration #1 is - 9232.62
Iteration: 1
Primal iterate: [2308.15382761 6924.4615058 ]
Flattened Jacobian: [ 1 -1]
Dual infeasibility: [-3807.1261665 -5330.17863752]
Objective value at iteration #2 is - 32831.6
Iteration: 2
Primal iterate: [ 9283.95016194 23547.67587445]
Flattened Jacobian: [ 1 -1]
Dual infeasibility: [-10191.60234577 -13407.40835721]
Objective value at iteration #3 is - 34372.2

The iterations continued and reached 3000 steps and the final answer is this:

Objective value at iteration #3000 is - 28980.6
Iteration: 3000
Primal iterate: [ 6848.26950247 22132.29693556]
Flattened Jacobian: [ 1 -1]
Dual infeasibility: [0.99999354 0.99999283]

What is going on? I don't see any mistakes in my code. Could it be this simple problem is not suitable for ipopt? Or are there any bugs in cyipopt?

I hope someone can help me with this confusion. Helps are appreciated!