Why optimization finds best solutions in SciPy - See It in Action

Why optimization finds best solutions

📖 Scenario: Imagine you want to find the lowest point in a hilly park. Optimization helps us find that lowest point by trying different paths and checking heights.

🎯 Goal: You will create a simple function, set a starting point, use optimization to find the lowest value, and then print the best solution found.

📋 What You'll Learn

Create a function called hill that returns the value of (x-3)**2 + 4

Create a variable called start_point and set it to 0

Use scipy.optimize.minimize with hill and start_point to find the minimum

Print the x value and the minimum function value found by the optimizer

💡 Why This Matters

🌍 Real World

Optimization helps in many areas like finding the cheapest cost, best route, or best settings for machines.

💼 Career

Understanding optimization is key for data scientists to improve models and make smart decisions automatically.

1

Create the function to optimize

Create a function called hill that takes one input x and returns the value of (x-3)**2 + 4.

SciPy

# Define the function hill(x) that returns (x-3)**2 + 4
# Your code here

Need a hint?

This function looks like a bowl shape with its lowest point at x=3.

2

Set the starting point for optimization

Create a variable called start_point and set it to 0.

SciPy

def hill(x):
    return (x - 3)**2 + 4

# Set start_point to 0
# Your code here

Need a hint?

Start the search from zero to see how optimization moves towards the best solution.

3

Use optimization to find the minimum

Import minimize from scipy.optimize. Use minimize with the function hill and the start_point to find the minimum. Save the result in a variable called result.

SciPy

def hill(x):
    return (x - 3)**2 + 4

start_point = 0

# Import minimize and find the minimum of hill starting at start_point
# Your code here

Need a hint?

Use minimize to let the computer find the lowest point of the hill function.

4

Print the best solution found

Print the x value where the minimum occurs using result.x and the minimum function value using result.fun.

SciPy

from scipy.optimize import minimize

def hill(x):
    return (x - 3)**2 + 4

start_point = 0

result = minimize(hill, start_point)

# Print the x value and function value of the minimum
# Your code here

Need a hint?

The optimizer finds the x that makes the function smallest, which should be near 3.