SciPy — Optimization

Scalar optimization

from scipy.optimize import minimize_scalar

def f(x):
    return (x - 3)**2 + 2

result = minimize_scalar(f)
print(f"Minimum at x = {result.x:.2f}")
print(f"Minimum value = {result.fun:.2f}")

Bounded optimization

result = minimize_scalar(f, bounds=(0, 5), method='bounded')
print(f"Minimum in [0,5]: x = {result.x:.2f}")

Multivariate optimization

from scipy.optimize import minimize

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

x0 = [0, 0]
result = minimize(objective, x0, method='L-BFGS-B')
print(f"Optimal: x = {result.x}")

Constrained optimization

from scipy.optimize import minimize

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

constraints = [
    {'type': 'eq', 'fun': lambda x: x[0] + x[1] - 1}
]

result = minimize(objective, [0, 0], constraints=constraints)
print(f"Optimal: x = {result.x}")

Curve fitting

from scipy.optimize import curve_fit
import numpy as np

def model(x, a, b):
    return a * np.exp(b * x)

x = np.array([0, 1, 2, 3, 4])
y = np.array([1, 2.7, 7.4, 20.1, 54.6])

popt, pcov = curve_fit(model, x, y)
print(f"a = {popt[0]:.2f}, b = {popt[1]:.2f}")

Root finding

from scipy.optimize import fsolve

def f(x):
    return x**2 - 4

root = fsolve(f, 1)
print(f"Root: {root[0]:.2f}")

Mini Practice

1. Find minimum of a function
2. Optimize with constraints
3. Fit a curve to data
4. Find roots of an equation

Up Next

Continue with Interpolation - Estimating values.