Perform optimization using SciPy's optimize module to find function minimum

Last update on March 27 2025 09:14:12 (UTC/GMT +8 hours)

14. Optimization with SciPy's Optimize Module

Write a NumPy program to generate a set of points and perform optimization using SciPy's optimize module to find the minimum of a function.

Sample Solution:

Python Code:

import numpy as np  # Import NumPy library
from scipy.optimize import minimize  # Import minimize function from SciPy's optimize module

# Define the function to be minimized
def objective_function(x):
    return x[0]**2 + x[1]**2 + 3 * np.sin(x[0]) * np.cos(x[1])

# Generate a set of initial points
initial_guess = np.array([1.0, 1.0])

# Perform optimization using SciPy's minimize function
result = minimize(objective_function, initial_guess, method='BFGS')

# Print the optimization results
print("Optimization Result:")
print("Minimum Value of the Function:", result.fun)
print("Point at Minimum:", result.x)
print("Number of Iterations Performed:", result.nit)
print("Convergence Status:", result.success)
print("Optimization Message:", result.message)

Output:

Optimization Result:
Minimum Value of the Function: -1.5404628057094898
Point at Minimum: [-9.14856375e-01 -6.01451321e-08]
Number of Iterations Performed: 8
Convergence Status: True
Optimization Message: Optimization terminated successfully.

Explanation:

• Import libraries:
• Import the NumPy library for numerical operations.
• Import the minimize function from SciPy's optimize module for performing optimization.
• Define the Objective Function:
• Create the function objective_function(x) to be minimized. This function takes a point x (array of coordinates) as input and returns the function value.
• Generate Initial Points:
• Define an initial guess as a NumPy array [1.0, 1.0] for the starting point of the optimization algorithm.
• Perform optimization:
• Use the minimize function from SciPy to find the minimum of the objective function starting from the initial guess. The method parameter is set to 'BFGS', a popular optimization algorithm.
• Finally print the results of the optimization, including:
• The minimum value of the function (result.fun).
• The point at which the minimum occurs (result.x).
• The number of iterations performed (result.nit).
• The convergence status (result.success).
• The optimization message (result.message).

For more Practice: Solve these Related Problems:

• Write a Numpy program to generate a set of points and use SciPy's optimize.minimize to find the minimum of a nonlinear function.
• Write a Numpy program to apply SciPy's optimize.curve_fit to a noisy dataset and compare the optimized parameters with theoretical values.
• Write a Numpy program to use SciPy's optimize.root to solve a system of nonlinear equations derived from generated data.
• Write a Numpy program to implement constrained optimization on a function using SciPy's optimize.minimize with bounds.

Python-Numpy Code Editor:

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