CVXPY
Maximize
  Sum(x @ [ 1.00001 -0.99999], None, False)
Subject To
 14: norm1(x) <= 1.4142135623730951
Bounds
 x free
End
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AFTER COMPILATION
Minimize
  - 1.00001 C0 + 0.99999 C1
Subject To
 R0: C0 - C2 <= 0
 R1: C1 - C3 <= 0
 R2: - C0 - C2 <= 0
 R3: - C1 - C3 <= 0
 R4: C2 + C3 <= 1.414213562373095
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
End
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GUROBI
Maximize
  1.00001 x[0] - 0.99999 x[1]
Subject To
 14: norm1_1 <= 1.414213562373095
Bounds
 x[0] free
 x[1] free
General Constraints
 GC0: norm1_1 = NORM ( 1 ) ( x[0] , x[1] )
End