Minimizing multivariate functions (minimize) in SciPy - Mini Project: Build & Apply

Minimizing Multivariate Functions with scipy.optimize.minimize

📖 Scenario: Imagine you are a gardener trying to find the best spot in your garden to plant a new tree. The best spot is where the soil is just right, not too dry and not too wet. We can think of this as finding the lowest point on a bumpy surface that represents soil quality. In this project, you will learn how to find the lowest point of a mathematical function with many variables using Python.

🎯 Goal: You will build a simple program that uses scipy.optimize.minimize to find the minimum value of a function with two variables. This will help you understand how to use optimization tools to solve real-world problems.

📋 What You'll Learn

Create a function that takes two variables and returns a value

Set an initial guess for the variables

Use scipy.optimize.minimize to find the minimum of the function

Print the result showing the minimum point and minimum value

💡 Why This Matters

🌍 Real World

Optimization is used in many fields like engineering, economics, and machine learning to find the best solutions under given conditions.

💼 Career

Knowing how to minimize functions helps in roles like data scientist, operations researcher, and any job involving decision making or model fitting.

1

Define the function to minimize

Create a function called soil_quality that takes a variable x (a list or array with two numbers) and returns the value of the function (x[0] - 3)**2 + (x[1] + 1)**2 + 5.

SciPy

# Define the function soil_quality with input x
# Your code here

Need a hint?

This function calculates how good the soil is at point x. The goal is to find the x that makes this value as small as possible.

2

Set the initial guess for variables

Create a variable called initial_guess and set it to the list [0, 0] as the starting point for the minimization.

SciPy

def soil_quality(x):
    return (x[0] - 3)**2 + (x[1] + 1)**2 + 5

# Set the initial guess for the variables
# Your code here

Need a hint?

The initial guess is where the program starts looking for the minimum.

3

Use scipy.optimize.minimize to find the minimum

Import minimize from scipy.optimize. Then create a variable called result and set it to the output of minimize with arguments soil_quality and initial_guess.

SciPy

def soil_quality(x):
    return (x[0] - 3)**2 + (x[1] + 1)**2 + 5

initial_guess = [0, 0]

# Import minimize and find the minimum
# Your code here

Need a hint?

The minimize function tries to find the values of x that make soil_quality as small as possible.

4

Print the minimum point and minimum value

Print the minimum point found by accessing result.x and the minimum value by accessing result.fun.

SciPy

from scipy.optimize import minimize

def soil_quality(x):
    return (x[0] - 3)**2 + (x[1] + 1)**2 + 5

initial_guess = [0, 0]

result = minimize(soil_quality, initial_guess)

# Print the minimum point and minimum value
# Your code here

Need a hint?

The minimum point is where the function is smallest. The minimum value is the function's value at that point.