Error in Defintion of Rosenbrock Function

[rshanker779]

The Rosenbrock function in the docs is incorrectly defined.
This occurs in the section Constrained minimization of multivariate scalar functions at https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html
The correct definition is on wikipedia: https://en.wikipedia.org/wiki/Rosenbrock_function.

The definition used in docs is:

100 * (x_0 - x_1 ^2) ^2 + (1 - x_0) ^2

which should be

100 * (x_1 - x_0 ^2) ^2 + (1 - x_0) ^2

As a verification, this block of code (with index swapped) gives the minimum as defined in the docs.

Reproducing code example:

from scipy.optimize import minimize

def rosenbrock(x):
    return 100 * (x[1] - x[0]**2) ** 2 + (1 - x[0]) ** 2

ros_cons = [{'type': 'ineq', 'fun': lambda x: 1 - 2 * x[1] - x[0]},
            {'type': 'ineq', 'fun': lambda x: 1 - x[0] ** 2 - x[1]},
            {'type': 'ineq', 'fun': lambda x: 1 + x[1] - x[0] ** 2},
            {'type': 'eq', 'fun': lambda x: 2 * x[0] + x[1] - 1}]
opt_res = minimize(rosenbrock, x0=[2, -1], constraints=ros_cons, bounds=[(0, 1), (-0.5, 2)])```
print(opt_res.x)

[0.41494395 0.17011211]

Scipy/Numpy/Python version information:

import sys, scipy, numpy; print(scipy.__version__, numpy.__version__, sys.version_info)

1.1.0 1.15.1 sys.version_info(major=3, minor=6, micro=5, releaselevel='final', serial=0)

[ilayn]

@rshanker779 Thanks for reporting. Do you mind submitting a PR? We are about to make a new release (tomorrowish) and this would be nice to have it.

[rshanker779]

Not a problem, will do.