Constraints and bounds

Real optimizers enforce box bounds (each variable in [low, high]) and sometimes linear/nonlinear constraints—essential for physically plausible parameters.

Bounds format

For minimize with method='L-BFGS-B', pass bounds=[(0, None), (-5, 5)] per variable. Use None for open ends.

Constraints dict

• type='ineq' — c(x) ≥ 0
• type='eq' — c(x) = 0
• Methods: SLSQP, trust-constr

Bounded example

import numpy as np
from scipy import optimize

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

bounds = [(0, 1), (0, 1)]  # box [0,1] x [0,1]
res = optimize.minimize(f, [0.5, 0.5], method='L-BFGS-B', bounds=bounds)
print(res.x)

Important interview questions and answers

1. Q: Why bounds in ML?
   A: Keep weights or probabilities in valid ranges—e.g. non-negative concentrations.
2. Q: L-BFGS-B?
   A: Limited-memory BFGS with box constraints—workhorse for bounded ML-style problems.

Self-check

1. How do you pass bounds to minimize?
2. What does an inequality constraint mean in SciPy's convention?

Tip: Use L-BFGS-B when parameters must stay in a box (probabilities, physical lengths).