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
OBJECTIVE
  Sense            : minimize
VARIABLES
  [continuous] <x_0>: obj=-1, original bounds=[-inf,+inf]
  [continuous] <x_1>: obj=-1, original bounds=[-inf,+inf]
  [continuous] <x_2>: obj=-1, original bounds=[-inf,+inf]
  [continuous] <x_3>: obj=-1, original bounds=[-inf,+inf]
  [continuous] <x_4>: obj=0, original bounds=[-inf,+inf]
  [continuous] <x_5>: obj=0, original bounds=[-inf,+inf]
  [continuous] <x_6>: obj=0, original bounds=[-inf,+inf]
  [continuous] <x_7>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_8>: obj=0, original bounds=[0,+inf]
  [continuous] <soc_t_9>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_10>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_11>: obj=0, original bounds=[0,+inf]
  [continuous] <soc_t_12>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_13>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_14>: obj=0, original bounds=[0,+inf]
  [continuous] <soc_t_15>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_16>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_17>: obj=0, original bounds=[0,+inf]
  [continuous] <soc_t_18>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_19>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <c1>:  -<x_0>[C] <= 0;
  [linear] <c2>:  -<x_1>[C] <= 0;
  [linear] <c3>:  -<x_2>[C] <= 0;
  [linear] <c4>:  -<x_3>[C] <= 0;
  [linear] <c5>: <x_4>[C] <= 1;
  [linear] <c6>: <x_5>[C] <= 1;
  [linear] <c7>: <x_6>[C] <= 1;
  [linear] <c8>: <x_7>[C] <= 1;
  [linear] <c9>: <soc_t_8>[C] -<x_4>[C] == 1;
  [linear] <c10>: <soc_t_9>[C] -<x_4>[C] == -1;
  [linear] <c11>: <soc_t_10>[C] -2<x_0>[C] == 0;
  [nonlinear] <c12>: <soc_t_9>*<soc_t_9>+<soc_t_10>*<soc_t_10>-<soc_t_8>*<soc_t_8> <= 0;
  [linear] <c13>: <soc_t_11>[C] -<x_5>[C] == 1;
  [linear] <c14>: <soc_t_12>[C] -<x_5>[C] == -1;
  [linear] <c15>: <soc_t_13>[C] -2<x_1>[C] == 0;
  [nonlinear] <c16>: <soc_t_12>*<soc_t_12>+<soc_t_13>*<soc_t_13>-<soc_t_11>*<soc_t_11> <= 0;
  [linear] <c17>: <soc_t_14>[C] -<x_6>[C] == 1;
  [linear] <c18>: <soc_t_15>[C] -<x_6>[C] == -1;
  [linear] <c19>: <soc_t_16>[C] -2<x_2>[C] == 0;
  [nonlinear] <c20>: <soc_t_15>*<soc_t_15>+<soc_t_16>*<soc_t_16>-<soc_t_14>*<soc_t_14> <= 0;
  [linear] <c21>: <soc_t_17>[C] -<x_7>[C] == 1;
  [linear] <c22>: <soc_t_18>[C] -<x_7>[C] == -1;
  [linear] <c23>: <soc_t_19>[C] -2<x_3>[C] == 0;
  [nonlinear] <c24>: <soc_t_18>*<soc_t_18>+<soc_t_19>*<soc_t_19>-<soc_t_17>*<soc_t_17> <= 0;
END
----------------------------------------
SCIP
OBJECTIVE
  Sense            : maximize
VARIABLES
  [continuous] <y_0_0>: obj=1, original bounds=[0,+inf]
  [continuous] <y_0_1>: obj=1, original bounds=[0,+inf]
  [continuous] <y_1_0>: obj=1, original bounds=[0,+inf]
  [continuous] <y_1_1>: obj=1, original bounds=[0,+inf]
CONSTRAINTS
  [nonlinear] <15_0_0>: <y_0_0>*<y_0_0> <= 1;
  [nonlinear] <15_0_1>: <y_0_1>*<y_0_1> <= 1;
  [nonlinear] <15_1_0>: <y_1_0>*<y_1_0> <= 1;
  [nonlinear] <15_1_1>: <y_1_1>*<y_1_1> <= 1;
END