CVXPY
Minimize
  Pnorm(X + -[[2.00 1.00]
 [-2.00 -4.00]], 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 = -2
 c3: +1 soc_t_2 -1 x_2 = +2
 c4: +1 soc_t_3 -1 x_3 = -1
 c5: +1 soc_t_4 -1 x_4 = +4
 c6: + [ +1 soc_t_1 * soc_t_1 +1 soc_t_2 * soc_t_2 +1 soc_t_3 * soc_t_3 +1 soc_t_4 * soc_t_4 -1 soc_t_0 * soc_t_0
 ] <= +0
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 soc_t_1 free
 soc_t_2 free
 soc_t_3 free
 soc_t_4 free
End
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SCIP
Minimize
 Obj: +1 x5
Subject to
\   [nonlinear] <c1>: ((<X_0_0>*<X_0_0>+<X_0_0>*(-4)+<X_0_1>*<X_0_1>+<X_0_1>*(-2)+<X_1_0>*<X_1_0>+<X_1_0>*4+<X_1_1>*<X_1_1>+<X_1_1>*8+25))^0.5+<x5>*(-1) <= 0;
Bounds
 X_0_0 free
 X_0_1 free
 X_1_0 free
 X_1_1 free
 x5 free
End