Method selection (Nelder-Mead, BFGS, Powell) in SciPy - Mini Project: Build & Apply

Method selection (Nelder-Mead, BFGS, Powell)

📖 Scenario: You are helping a small business find the best price to maximize their profit. They have a simple profit function that depends on the price. You will use different methods to find the price that gives the highest profit.

🎯 Goal: Learn how to use three optimization methods: Nelder-Mead, BFGS, and Powell from scipy.optimize.minimize to find the best price that maximizes profit.

📋 What You'll Learn

Create a profit function that depends on price

Set an initial guess for the price

Use scipy.optimize.minimize with methods Nelder-Mead, BFGS, and Powell

Print the best price and maximum profit found by each method

💡 Why This Matters

🌍 Real World

Businesses often need to find the best price or settings to maximize profit or minimize cost. Optimization methods help find these values efficiently.

💼 Career

Data scientists and analysts use optimization techniques to solve real problems in pricing, resource allocation, and machine learning model tuning.

1

Create the profit function

Create a function called profit that takes a single variable price and returns the negative of the profit calculated as -(price * (100 - 2 * price)). This means profit = price times (100 minus 2 times price), and we negate it because scipy.optimize.minimize finds minimum values.

SciPy

# Your code here
def profit(price):
    pass

Need a hint?

Think of profit as price times quantity sold. Quantity decreases as price increases. We use negative because the optimizer finds minimum, but we want maximum profit.

2

Set the initial guess for price

Create a variable called initial_price and set it to 10. This is the starting point for the optimization methods.

SciPy

def profit(price):
    return -(price * (100 - 2 * price))

# Your code here

Need a hint?

Just create a variable named initial_price and assign it the value 10.

3

Use optimization methods to find best price

Import minimize from scipy.optimize. Use minimize three times with the profit function and initial_price. Use methods 'Nelder-Mead', 'BFGS', and 'Powell'. Save the results in variables result_nm, result_bfgs, and result_powell respectively.

SciPy

def profit(price):
    return -(price * (100 - 2 * price))

initial_price = 10

# Your code here

Need a hint?

Use minimize(profit, initial_price, method='MethodName') for each method and save the results.

4

Print the best price and maximum profit from each method

Print the best price and maximum profit found by each method. Use result_nm.x[0], result_bfgs.x[0], and result_powell.x[0] for prices. Calculate profit by calling -profit(price) because profit function returns negative. Print results with labels: 'Nelder-Mead', 'BFGS', and 'Powell'.

SciPy

from scipy.optimize import minimize

def profit(price):
    return -(price * (100 - 2 * price))

initial_price = 10

result_nm = minimize(profit, initial_price, method='Nelder-Mead')
result_bfgs = minimize(profit, initial_price, method='BFGS')
result_powell = minimize(profit, initial_price, method='Powell')

# Your code here

Need a hint?

Use print(f"Method best price: {result.x[0]:.2f}, max profit: {-profit(result.x[0]):.2f}") for each result.