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from lpfgopt import minimize
import matplotlib.pyplot as plt

# set up the objective funciton, 
# constraint fuction and bounds
f = lambda x: sum([i**2 for i in x])
g = lambda x: -x[0]**2 + 10 - x[1] 
bounds = [[-5,5] for i in range(2)]

# run the optimization
sol = minimize(f, bounds, fconstraint=g)['x']
print(f"Solution is: {sol}")

# plot the results on a contour plot
gg = lambda x: -x**2 + 10 # for plotting purposes

plt.figure(figsize=(8,8))
x, y = np.linspace(-5,5,1000), np.linspace(-5,5,1000)
X, Y = np.meshgrid(x,y)
Z = f([X,Y])

plt.contourf(X,Y,Z)
plt.plot(x, gg(x), "r", label="constraint")
plt.plot(*sol, 'x', 
         markersize=14, 
         markeredgewidth=4, 
         color="lime", 
         label="optimum")
plt.ylim(-5,5)
plt.xlim(-5,5)
plt.legend()
plt.show()









    



---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
<ipython-input-1-16e93bc80cff> in <module>
----> 1 from lpfgopt import minimize
      2 import matplotlib.pyplot as plt
      3 
      4 # set up the objective funciton,
      5 # constraint fuction and bounds

ModuleNotFoundError: No module named 'lpfgopt'