#!/usr/bin/env python
# coding: utf-8

# In[1]:


import pandas as pd
import numpy as np
from scipy.optimize import minimize


# Example:
# 
# Objective Function:
# $$
# \min x^2_1 + x_1 \times x_2
# $$
# s.t. Constraints:
# 
# $$
# \begin{aligned}
# x^3_1 + x_1 \times x_2 & = 100 \\
# x^2_1 + x_2 \leq 50 \\
# -100 \leq x_1, x_2 & \le 100
# \end{aligned}
# $$

# In[2]:


# define the objective function and constraints
def objective_fcn(x):
    # parameters:
    x1 = x[0]
    x2 = x[1]
    return x1**2 + x1 * x2

def equality_constraint(x):
    x1 = x[0]
    x2 = x[1]
    return x1**3 + x1 * x2 - 100   # Remember that we need to put everything from the RHS to the LHS so its = 0

def inequality_constraint(x):
    x1 = x[0]
    x2 = x[1]
    return x1**2 + x2 - 50

# Note: could also make all of these lambda functions

bounds_x1 = (-100, 100)
bounds_x2 = (-100, 100)
# we need to make it into a list
bounds = [bounds_x1, bounds_x2]

# we need to define the equality types 
constraint1 = {'type': 'eq', 'fun': equality_constraint}
constraint2 = {'type': 'ineq', 'fun': inequality_constraint}

constraints = [constraint1, constraint2]

# finally, give an initial value for x0. As long as it's reasonable, any pairs of numbers in between the
# bounds should be ok
x0 = [1,1]

# now we apply the minimization function. 
# scipy.optimize.minimize(fun, x0, method, bounds, constraints)

result = minimize(objective_fcn, x0, method='SLSQP', bounds=bounds, constraints=constraints)


# In[3]:


result


# The result returns:
# * fun = values of objective function
# * jac = jacobian
# * message = description of the cause of the termination
# * nfev, njev = No. of evaluations of the objective functions and of its Jacobian
# * nit = NO. of iterations
# * status, success = Termination and exit status
# * x = Solution of the optimization

# In[ ]: