CVXPY
Minimize
  Pnorm(x, 2) + Pnorm([ 1.00005 -0.99995], 2)
Subject To
Bounds
 x free
End
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AFTER COMPILATION
Minimize
 Obj: +1 x_0
Subject to
 c1: +1 soc_t_0 -1 x_0 = +0
 c2: +1 soc_t_1 -1 x_1 = +0
 c3: +1 soc_t_2 -1 x_2 = +0
 c4: + [ +1 soc_t_1 * soc_t_1 +1 soc_t_2 * soc_t_2 -1 soc_t_0 * soc_t_0 ] <= +0
Bounds
 x_0 free
 x_1 free
 x_2 free
 soc_t_1 free
 soc_t_2 free
End
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SCIP
Minimize
 Obj: +1 x3
Subject to
\   [nonlinear] <c1>: ((<x_0>*<x_0>+<x_1>*<x_1>))^0.5+<x3>*(-1)+1.41421356414086 <= 0;
Bounds
 x_0 free
 x_1 free
 x3 free
End