Minimizing scalar functions (minimize_scalar) in SciPy

Introduction

We use minimize_scalar to find the smallest value of a simple function. It helps us solve problems where we want to reduce cost, error, or any number to its lowest point.

Finding the best price to sell a product to maximize profit.

Minimizing the error in a simple prediction model.

Finding the shortest distance in a simple path problem.

Optimizing a single variable like time or temperature for best results.

Syntax

SciPy

from scipy.optimize import minimize_scalar

result = minimize_scalar(function, bounds=(lower, upper), method='bounded')

The function is what you want to minimize. It must take one number and return one number.

The bounds set the search limits. Use method='bounded' to respect these limits.

Examples

Minimize a simple parabola without bounds.

SciPy

from scipy.optimize import minimize_scalar

def f(x):
    return (x - 3) ** 2

result = minimize_scalar(f)

Minimize the same function but only between 0 and 5.

SciPy

from scipy.optimize import minimize_scalar

def f(x):
    return (x - 3) ** 2

result = minimize_scalar(f, bounds=(0, 5), method='bounded')

Sample Program

This code finds the minimum of the function (x-2)^2 + 1. It prints the smallest value and where it happens.

SciPy

from scipy.optimize import minimize_scalar

def cost(x):
    return (x - 2) ** 2 + 1

result = minimize_scalar(cost)
print(f"Minimum value: {result.fun}")
print(f"At x = {result.x}")

Important Notes

The function should be smooth and have one clear minimum for best results.

If you know the range where the minimum is, use bounds and method='bounded' for faster and safer search.

The result object has useful info like result.x (location) and result.fun (minimum value).

Summary

minimize_scalar helps find the lowest point of a simple function with one variable.

You can run it with or without limits on the variable.

It returns the minimum value and where it happens.