CVXPY
Maximize
  Sum(x, None, False)
Subject To
 8: PowerApprox(x, 2.0) <= 1.0
Bounds
 0.0 <= x
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=0, original bounds=[-inf,+inf]
  [continuous] <x_3>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_4>: obj=0, original bounds=[0,+inf]
  [continuous] <soc_t_5>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_6>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_7>: obj=0, original bounds=[0,+inf]
  [continuous] <soc_t_8>: obj=0, original bounds=[-inf,+inf]
  [continuous] <soc_t_9>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <c1>:  -<x_0>[C] <= 0;
  [linear] <c2>:  -<x_1>[C] <= 0;
  [linear] <c3>: <x_2>[C] <= 1;
  [linear] <c4>: <x_3>[C] <= 1;
  [linear] <c5>: <soc_t_4>[C] -<x_2>[C] == 1;
  [linear] <c6>: <soc_t_5>[C] -<x_2>[C] == -1;
  [linear] <c7>: <soc_t_6>[C] -2<x_0>[C] == 0;
  [nonlinear] <c8>: <soc_t_5>*<soc_t_5>+<soc_t_6>*<soc_t_6>-<soc_t_4>*<soc_t_4> <= 0;
  [linear] <c9>: <soc_t_7>[C] -<x_3>[C] == 1;
  [linear] <c10>: <soc_t_8>[C] -<x_3>[C] == -1;
  [linear] <c11>: <soc_t_9>[C] -2<x_1>[C] == 0;
  [nonlinear] <c12>: <soc_t_8>*<soc_t_8>+<soc_t_9>*<soc_t_9>-<soc_t_7>*<soc_t_7> <= 0;
END
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SCIP
OBJECTIVE
  Sense            : maximize
VARIABLES
  [continuous] <x_0>: obj=1, original bounds=[0,+inf]
  [continuous] <x_1>: obj=1, original bounds=[0,+inf]
CONSTRAINTS
  [nonlinear] <8_0>: <x_0>*<x_0> <= 1;
  [nonlinear] <8_1>: <x_1>*<x_1> <= 1;
END