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I am trying to maximize certain logLikelihood function, given trajectory T and parameter tMax, with respect to set o 2d + 2d^2 parameters X, where d is fixed integer.

Each parameter valid range is (0, 10), with exception to parameters with indexes 2*i+1 for i in range(d) (using Python convention). For those, the valid range is (-10, 10). Additionally, I create linear constraints, that for each i in range(d) X[2 * i] + X[2 * i + 1] * (tMax + 1.0) >=0

Here is implementation:

# T given
tMax = 500.0
_d = 2

# part of gradient for constraint X[2 * i] + X[2 * i + 1] * (tMax + 1.0) for i fixed in range(_d)
def grad_for_i(i, d, t_max):
    g = np.zeros(2 * d + 2 * d**2)
    g[2 * i] = 1.0
    g[2 * i + 1] = t_max + 1.0

    return g

# array of zeros of lenght l with 1 on index j
def one_on_jth(j, l):
    r = [0.0 for _ in range(l)]
    r[j] = 1.0
    return r

new_lin_const = {
    'type': 'ineq',
    'fun' : lambda x: np.array(
        [x[2 * i] + x[2 * i + 1] * (tMax+ 1.0) for i in range(_d)] 
        + [x[j] for j in range(2*_d + 2*_d**2) if j not in [2 * i + 1 for i in range(_d)]]
        ),
    'jac' : lambda x: np.array(
        [grad_for_i(i, _d, tMax) for i in range(_d)]
         + [one_on_jth(j, 2*_d + 2*_d**2) for j in range(2*_d + 2*_d**2) if j not in [2 * i + 1 for i in range(_d)]]
        )
}

X0 = [1.0 for _ in range(2 * (_d ** 2) + 2 * _d)]
bds = [(0.0, 10.0) for _ in range(2 * (_d ** 2) + 2 * _d)]
        for i in range(_d):
            bds[2*i + 1] = (-10.0, 10.0)

res = optimize.minimize(lambda x, args: -logLikelihood (x, args[0], args[1]),
         constraints=new_lin_const, x0 = X0, args=([T, tMax]), method='SLSQP', options={'disp': True}, bounds=bds)

Procedures converges, but result given is out of linear constraints defined bounds:

print(res.x)
#array([ 1.38771114, -0.72145294,  1.3960635 , -0.22399423,  1.49987397,
#        1.45837707,  1.49958886,  1.45772475,  5.88312636,  5.83211339,
#        5.81175866,  5.67393651])

How is it possible, result is out of bounds?

Piotr Cukier
  • 52
  • 5
  • This isn't a minimal **reproducible** example (MWE). For instance, `T` and `logLikelihood` are missing. Please provide an MWE, otherwise, it's hard to help properly. In the meantime, you should have a look at the second summand of your constraint function, that doesn't make sense to me. By the way, your code is way too verbose (which is okay for a beginner), but it's highly recommended that you make yourself familiar with NumPy and its vectorized operations etc. – joni Sep 13 '22 at 15:14

0 Answers0