BUG:optimize: slsqp cannot handle badly scaled problem #3824
Description
Hi everybody,
I am quite sure there is a bug with SLSQP. Here is a minimal example:
import numpy as np
import scipy.optimize as scopt
def loss(x,r):
return -np.dot(x,r)
def opt(r):
r = np.array(r)
def cons(x):
return sum(x)
cons = [{'type': 'eq', 'fun': cons}]
x_init = [0., 0.]
x_opt = scopt.minimize(loss, x_init, method='SLSQP', constraints=cons, args = (r,))
return x_opt
Then for instance with r = [0., 0.01], opt(r) returns:
x: array([ -2.16178351e+08, 2.16178351e+08])
fun: -2161783.5125566297
message: 'Singular matrix C in LSQ subproblem'
njev: 17
nit: 17
nfev: 68
jac: array([ 0., 0., 0.])
status: 6
success: False
which is fine, because the solution is have the first component set to minus infinity and the second one to plus infinity. But with r = [0., 0.001], it returns:
x: array([ 0., 0.])
fun: -0
message: 'Optimization terminated successfully.'
njev: 1
nit: 1
nfev: 4
jac: array([ 0. , -0.001, 0. ])
status: 0
success: True
And it should have the same solution (or absence of solution). Putting a minimum or a maximum on the components of x does not change anything (that is, the first case finds a good solution and the second one returns the initial vector). Providing jacobians do not help either. It does seem like a bug to me...