SciPy minimize()

The minimize() function in the SciPy library is used to find the minimum of a scalar function. It provides various optimization algorithms, including both gradient-based and derivative-free methods.

Syntax

scipy.optimize.minimize(fun, x0, args=(), method=None, jac=None, hess=None, constraints=(), bounds=None, tol=None, options=None)

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Parameters

• fun: The objective function to be minimized.
• x0: Initial guess for the variables.
• args: Extra arguments passed to the objective function.
• method: The optimization method to use (e.g., 'BFGS', 'Nelder-Mead', 'Powell', etc.).
• jac (Optional): The gradient (Jacobian) of the objective function. If not provided, numerical differentiation is used.
• hess (Optional): The Hessian matrix of the objective function. Typically used with second-order methods like ‘Newton-CG’ or ‘trust-ncg’.
• constraints (Optional): Constraints definition. Can include equality or inequality constraints.
• bounds (Optional): Bounds on variables.
• tol (Optional): Tolerance for termination. Specifies the convergence threshold.
• options (Optional): A dictionary of additional options specific to the selected optimization method (e.g., maximum number of iterations, tolerance, etc.).

It returns an OptimizeResult object with the optimal solution, function value at the solution, success status, and other optimization details.

Example

In this example, we are using the minimize() function to find the minimum value of a quadratic objective function:

from scipy.optimize import minimize

# Define the objective function
def objective_function(x):
    return x**2

# Initial guess
x0 = 2

# Perform the minimization
result = minimize(objective_function, x0)

# Print the result
print("Optimal value:", result.fun)
print("Optimal point:", result.x)

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It produces the following output:

Optimal value: 3.5662963072207506e-16
Optimal point: [-1.88846401e-08]

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Codebyte Example

Run the following codebyte example to understand how the minimize() function works:

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