Optimization basics

scipy.optimize finds minima, maxima, and roots of scalar and vector functions—used in curve fitting, ML loss minimization, and engineering design after preparing NumPy inputs.

Core ideas

• Objective — scalar function f(x) to minimize
• Initial guess — starting point x₀ (quality matters)
• Method — algorithm (BFGS, Nelder-Mead, L-BFGS-B, etc.)
• Result object — x, fun, success, message

Scalar vs multivariate

• minimize_scalar — one variable, bracket or bounded
• minimize — vector x ∈ ℝⁿ
• Always check result.success and residuals

Hello minimize

import numpy as np
from scipy import optimize

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

res = optimize.minimize(f, x0=[0, 0], method='BFGS')
print('x:', res.x, 'f:', res.fun, 'success:', res.success)

Important interview questions and answers

1. Q: Local vs global minimum?
   A: Most methods find local minima—try multiple x₀ or global search for hard landscapes.
2. Q: Why BFGS?
   A: Popular quasi-Newton method for smooth unconstrained problems; no Hessian required.

Self-check

1. What four items define an optimization problem?
2. What attributes does minimize return?

Tip: Always print result.success and result.message after minimize.