I’m having trouble with global optimisation for a function that has specific constraints on the values. Let me explain the situation.

We have a function F(x1, x2,…, xn, a, b), and our goal is to find its global minimum. We also have constraints from physics: x[i] <= x[i+1] for all values of x. All values in x[i] and a,b have boundaries (0,1).

How can I set up the correct nonlinear constraint for x in SciPy?

I’ve already tried this option:

def con(x):
    out = np.ones(N)

    for i in range(N-1):
        if x[i] > x[i + 1]:
            out[i:] = -1
            return out
        else:
            out[i] = 1

    if x[N - 1] < x[N - 2]: 
        out[N - 1] = -1
    else:
        out[N - 1] = 1

    return out

const = NonlinearConstraint(con, 0, 1)

bounds = [(0, 1) for i in range(N+2)]

solution = differential_evolution(f, bounds, workers=-1, constraints=const)

But it doesn’t work. Some values in x are outside the bounds (< 0, how???) and it ignores the constraint x[i]<=x[i+1]. I think I completely misunderstand how the NonlinearConstraint works. I would appreciate any help!