code: 
  
  
  """
  In Class Ex:
  Constrained \infty-norm minimization
  
  Problem:
      minimize:
          \norm{x}_\infty
      subject to:
          A x \leq b
  
  Notes:
      \norm{x}_\infty = \max_i \abs{x_i}
                      = \max_i \{x_i, -x_i\}
                      = \max_i \{x_1, \dots, x_n, -x_1, \dots, -x_n\}
  
  Epigraph Form:
      minimize:
          t
      subject to:
          \max_i \{x_1, \dots, x_n, -x_1, \dots, -x_n\} \leq t
          Ax \leq b
  
  Equivelent Form:
      minimize:
          t
      subject to:
          x_i \leq t, i = 1, \dots, n
          -x_i \leq t, i = 1, \dots, n
          Ax \leq b
  
  Equivelent Form:
      minimize:
          t
      subject to:
          - 1 t \leq x \leq 1 t
          Ax \leq b
  """
  
  
  import cvxpy as cp
  import numpy as np
  
  
  n = 10
  m = 100
  
  A = np.random.rand(m, n)
  b = np.random.rand(m, 1) - 1
  
  
  X = cp.Variable((n, n))
  prob = cp.Problem(cp.Minimize(cp.max(cp.sum(cp.abs(X)))),
                    [A @ X <= b])
  
  
  # Print result.
  print("The optimal value is", prob.value)
  print("A solution X is")
  print(X.value)
  
  
  # doesn't work..... don't really feel like troubleshooting though
  
apis: numpy.random.rand