CVXPY
Minimize
  Sum(X, None, False)
Subject To
 52: 1.0 <= min(X + [[1.00 -2.00]
 [3.00 4.00]], None, False)
Bounds
 X free
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]
CONSTRAINTS
  [linear] <c1>:  -<x_0>[C] -<x_4>[C] <= 1;
  [linear] <c2>:  -<x_1>[C] -<x_4>[C] <= 3;
  [linear] <c3>:  -<x_2>[C] -<x_4>[C] <= -2;
  [linear] <c4>:  -<x_3>[C] -<x_4>[C] <= 4;
  [linear] <c5>: <x_4>[C] <= -1;
END
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SCIP
OBJECTIVE
  Sense            : minimize
VARIABLES
  [continuous] <X_0_0>: obj=1, original bounds=[-inf,+inf]
  [continuous] <X_0_1>: obj=1, original bounds=[-inf,+inf]
  [continuous] <X_1_0>: obj=1, original bounds=[-inf,+inf]
  [continuous] <X_1_1>: obj=1, original bounds=[-inf,+inf]
  [continuous] <min_1>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <min_1_0_0>: <X_0_0>[C] -<min_1>[C] >= -1;
  [linear] <min_1_0_1>: <X_0_1>[C] -<min_1>[C] >= 2;
  [linear] <min_1_1_0>: <X_1_0>[C] -<min_1>[C] >= -3;
  [linear] <min_1_1_1>: <X_1_1>[C] -<min_1>[C] >= -4;
  [linear] <52>: <min_1>[C] >= 1;
END