scipy.optimize.minimize：含numpy数组参数时如何指定边界

I'm using scipy.optimize.minimize for optimization calculations, here's my code:

sig_init = 2
b_init = np.array([0.2,0.01,0.5,-0.02])
params_init = np.array([b_init, sig_init])
mle_args = (y,x)
results = opt.minimize(crit, params_init, args=(mle_args))

The problem is that I need to set bounds for sig_init, but opt.minimize() requires bounds for each input parameter, and my input parameter includes a numpy array. How do I specify parameter bounds in this case?

First off, let's fix a critical detail in your parameter setup: right now, params_init is a nested structure (it holds a 4-element array and a scalar), but scipy.optimize.minimize expects a flat 1D array of individual parameters. This is a common gotcha—you'll need to flatten those values into a single sequence first.

Once that's sorted, setting bounds is straightforward: you just define bounds for each individual parameter in the flattened array, in order. Here's how to do it step by step:

1. Fix Your Initial Parameter Array #

Instead of wrapping b_init and sig_init into a nested array, concatenate them into a flat 1D array:

sig_init = 2
b_init = np.array([0.2, 0.01, 0.5, -0.02])
# Flatten into a single 1D array: [0.2, 0.01, 0.5, -0.02, 2]
params_init = np.concatenate([b_init, [sig_init]])

2. Define Bounds for Each Parameter #

The bounds argument accepts either a list of tuples or a Bounds object (from scipy.optimize). Let's assume you want no bounds on the b_init parameters, but need sig_init to be positive (a common requirement for standard deviation-like parameters):

Option 1: List of Tuples (Simple)

# First 4 parameters (b_init) have no bounds; 5th (sig_init) must be > 0
bounds = [(-np.inf, np.inf)] * 4 + [(0.0, np.inf)]

Option 2: Bounds Class (Cleaner for Larger Sets)

from scipy.optimize import Bounds

# Lower bounds: -infinity for b_init, 0 for sig_init
lower_bounds = [-np.inf] * 4 + [0.0]
# Upper bounds: infinity for all parameters
upper_bounds = [np.inf] * 5

bounds = Bounds(lower_bounds, upper_bounds)

3. Run the Minimization with Bounds #

Pass the bounds to the minimize function:

results = minimize(crit, params_init, args=mle_args, bounds=bounds)

Critical Note for Your Criterion Function #

Make sure your crit function expects a flat 1D array as input. Inside the function, you can split the parameters back into b and sig like this:

def crit(params, y, x):
    b = params[:4]  # First 4 elements are the b parameters
    sig = params[4] # 5th element is sig
    # ... rest of your MLE calculation ...

内容的提问来源于stack exchange，提问作者Stan Shunpike