How to perform constrained optimization with Sequential Least Squares Quadratic Programming in Python

In Python, you can perform constrained optimization using the Sequential Least Squares Quadratic Programming (SLSQP) algorithm with the scipy.optimize module. The minimize function in SciPy provides an option for constrained optimization, and you can set the method parameter to ‘SLSQP’ for SLSQP optimization.

Here’s an example of how to perform constrained optimization using the SLSQP algorithm in Python:

from scipy.optimize import minimize

# Define the objective function to minimize
def objective_function(x):
    return (x[0] - 2)**2 + (x[1] - 3)**2

# Define the equality constraint function
def equality_constraint(x):
    return x[0] + x[1] - 5

# Define the inequality constraint function
def inequality_constraint(x):
    return x[0] - 2*x[1]

# Set initial guess
initial_guess = [0, 0]

# Define the bounds for the variables
bounds = [(0, None), (0, None)]  # The bounds are set for x[0] and x[1]

# Perform constrained optimization using SLSQP
result = minimize(objective_function, initial_guess, method='SLSQP', bounds=bounds, constraints=[{'type': 'eq', 'fun': equality_constraint}, {'type': 'ineq', 'fun': inequality_constraint}])

# Display the result
print("Optimal values:", result.x)
print("Optimal objective function value:", result.fun)
print("Constraint results:", equality_constraint(result.x), inequality_constraint(result.x))

In this example:

• The objective_function is the function to minimize.
• The bounds variable defines the bounds for each variable. In this case, both x[0] and x[1] are non-negative ((0, None)).
• The equality_constraint and inequality_constraint functions represent the constraints. In this example, there is an equality constraint (x[0] + x[1] - 5) and an inequality constraint (x[0] - 2*x[1]).
• The method='SLSQP' parameter specifies the SLSQP optimization algorithm.

Make sure to adapt the objective function and constraints according to your specific problem. Additionally, provide appropriate bounds for the variables in the bounds parameter. The constraints parameter is a list containing dictionaries specifying the type and function of each constraint.

Always refer to the SciPy documentation for the most up-to-date information on optimization methods and their parameters.