My First Robust Problem

We consider a simple linear optimization problem with an ellipsoidal uncertainty set. (TODO complete)

import cvxpy as cp
import numpy as np
import lropt as lr

n = 2
P = np.array([[1.,2],[1.,0.]])
A = np.eye(2)
b = np.zeros(2)
c = np.array([2,1])
a = np.array([.4,0.5])

u = lr.UncertainParameter(n,
                          uncertainty_set=lr.Ellipsoidal(A=A, b=b))

x = cp.Variable(n)

objective = cp.Minimize(c @ x)
constraints = [(P @ u + a) @ x <= 10]

prob = lr.RobustProblem(objective, constraints)

prob.solve()

print("optimal value = ", objective.value)
print("optimal solution = ", x.value)

optimal value =  -20.76298271930384
optimal solution =  [ -1.83921308 -17.08455655]