Minimizing scalar functions (minimize_scalar) in SciPy - Mini Project: Build & Apply

Minimizing Scalar Functions with scipy.optimize.minimize_scalar

📖 Scenario: Imagine you are helping a small business find the best price to maximize their profit. The profit depends on the price, and you want to find the price that gives the lowest cost or highest profit loss. We will use a simple math function to represent this and find the minimum point.

🎯 Goal: You will create a function that calculates cost based on price, then use scipy.optimize.minimize_scalar to find the price that minimizes this cost.

📋 What You'll Learn

Create a function named cost_function that takes one argument x and returns (x - 3) ** 2 + 5.

Import minimize_scalar from scipy.optimize.

Use minimize_scalar to find the minimum of cost_function.

Store the result in a variable named result.

Print the minimum value found using result.fun and the location of the minimum using result.x.

💡 Why This Matters

🌍 Real World

Businesses often want to find the best price or quantity to minimize costs or maximize profits. Minimizing scalar functions helps find these optimal points quickly.

💼 Career

Data scientists and analysts use optimization techniques like <code>minimize_scalar</code> to solve real-world problems in finance, marketing, engineering, and more.

1

Create the cost function

Create a function called cost_function that takes one argument x and returns the value of (x - 3) ** 2 + 5.

SciPy

# Define the cost_function that calculates (x - 3) ** 2 + 5
# Your code here

Need a hint?

Remember to use def to create a function and return the expression (x - 3) ** 2 + 5.

2

Import minimize_scalar

Import minimize_scalar from the scipy.optimize module.

SciPy

def cost_function(x):
    return (x - 3) ** 2 + 5

# Import minimize_scalar from scipy.optimize
# Your code here

Need a hint?

Use the syntax from scipy.optimize import minimize_scalar to import the function.

3

Find the minimum using minimize_scalar

Use minimize_scalar with the cost_function to find the minimum. Store the result in a variable called result.

SciPy

from scipy.optimize import minimize_scalar

def cost_function(x):
    return (x - 3) ** 2 + 5

# Use minimize_scalar with cost_function and store in result
# Your code here

Need a hint?

Call minimize_scalar with cost_function as the argument and assign it to result.

4

Print the minimum value and location

Print the minimum value found using result.fun and the location of the minimum using result.x. Use two separate print statements.

SciPy

from scipy.optimize import minimize_scalar

def cost_function(x):
    return (x - 3) ** 2 + 5

result = minimize_scalar(cost_function)

# Print the minimum value and the location of the minimum
# Your code here

Need a hint?

Use print(result.fun) to show the minimum value and print(result.x) to show where it happens.