Optimization with scipy.optimize

The scipy.optimize module provides tools for finding optimal values of functions and solving equations.

It’s widely used in scientific computing, engineering, and data analysis to:

• Minimize or maximize mathematical functions
• Fit models or curves to data
• Solve equations or systems of equations numerically

First, import the necessary libraries:

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import numpy as np
from scipy import optimize

Use optimize.minimize() to find the minimum value of a mathematical function.

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# Define a function: f(x) = x^2 + 5*sin(x)
def func(x):
    return x**2 + 5*np.sin(x)

# Find the minimum starting from an initial guess
result = optimize.minimize(func, x0=2)

print("Optimal x value:", result.x[0])
print("Function value at optimum:", result.fun)

• func(x) — the objective function to minimize
• x0 — the initial guess for x
• The result object (result) contains both the optimal value of x and the minimum function value

Use optimize.root() to find the roots of equations, i.e., the points where a function equals zero.

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# Equation: cos(x) - x = 0
def equation(x):
    return np.cos(x) - x

root_result = optimize.root(equation, x0=0.5)

print("Root found at:", root_result.x[0])

• Here, we’re solving the equation cos(x) = x.
• The root() function searches for the value of x where the function output equals zero — the mathematical root.