CVXPY
Maximize
  Sum(y, None, False)
Subject To
 15: PowerApprox(y, 2.0) <= 1.0
Bounds
 0.0 <= y
End
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AFTER COMPILATION
Minimize
  - x_0 - x_1 - x_2 - x_3
Subject To
 R0: x_4 <= 1
 R1: x_5 <= 1
 R2: x_6 <= 1
 R3: x_7 <= 1
 R4: - x_4 + soc_t_4 = 1
 R5: - x_4 + soc_x_5 = -1
 R6: - 2 x_0 + soc_x_6 = 0
 R7: - x_5 + soc_t_7 = 1
 R8: - x_5 + soc_x_8 = -1
 R9: - 2 x_1 + soc_x_9 = 0
 R10: - x_6 + soc_t_10 = 1
 R11: - x_6 + soc_x_11 = -1
 R12: - 2 x_2 + soc_x_12 = 0
 R13: - x_7 + soc_t_13 = 1
 R14: - x_7 + soc_x_14 = -1
 R15: - 2 x_3 + soc_x_15 = 0
 qc0: [ - soc_t_4 ^2 + soc_x_5 ^2 + soc_x_6 ^2 ] <= 0
 qc1: [ - soc_t_7 ^2 + soc_x_8 ^2 + soc_x_9 ^2 ] <= 0
 qc2: [ - soc_t_10 ^2 + soc_x_11 ^2 + soc_x_12 ^2 ] <= 0
 qc3: [ - soc_t_13 ^2 + soc_x_14 ^2 + soc_x_15 ^2 ] <= 0
Bounds
 x_4 free
 x_5 free
 x_6 free
 x_7 free
 soc_x_5 free
 soc_x_6 free
 soc_x_8 free
 soc_x_9 free
 soc_x_11 free
 soc_x_12 free
 soc_x_14 free
 soc_x_15 free
End
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GUROBI
Maximize
  y[0,0] + y[0,1] + y[1,0] + y[1,1]
Subject To
 15[0,0]: [ y[0,0] ^2 ] <= 1
 15[0,1]: [ y[0,1] ^2 ] <= 1
 15[1,0]: [ y[1,0] ^2 ] <= 1
 15[1,1]: [ y[1,1] ^2 ] <= 1
Bounds
End