Support norm1 atom (#35)

Gurobi only handles vector norms, so we have to ensure we always use 1D
arrays when forwarding to `numpy` and/or `cvxpy` since they also have
matrix norms.

Part of #23

src/cvxpy_gurobi/__init__.py

@@ -599,6 +599,15 @@ def visit_multiply(self, mul: multiply) -> Any:
     def visit_NegExpression(self, node: NegExpression) -> Any:
         return -self.visit(node.args[0])
 
+    def visit_norm1(self, node: cp.norm1) -> Any:
+        (x,) = node.args
+        if isinstance(x, cp.Constant):
+            return np.linalg.norm(x.value.ravel(), 1)
+        arg = self.translate_into_variable(x)
+        varargs = [arg] if isinstance(arg, gp.Var) else arg.reshape(-1).tolist()
+        norm = gp.norm(varargs, 1)
+        return self.make_auxilliary_variable_for(norm, "norm1", lb=0)
+
     def visit_power(self, node: power) -> Any:
         power = self.visit(node.p)
         if power != 2:

tests/snapshots/all__lp_genexpr_norm1_0__0.txt

@@ -0,0 +1,28 @@
+CVXPY
+Minimize
+  norm1(x)
+Subject To
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0
+Subject To
+ R0: - C0 + C1 <= 0
+ R1: - C0 - C1 <= 0
+Bounds
+ C0 free
+ C1 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 x + norm1_1
+Subject To
+Bounds
+ x free
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( x )
+End

tests/snapshots/all__lp_genexpr_norm1_10__0.txt

@@ -0,0 +1,34 @@
+CVXPY
+Minimize
+  norm1(x) + norm1([ 1. -2.])
+Subject To
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0 + C1
+Subject To
+ R0: - C0 + C2 <= 0
+ R1: - C1 + C3 <= 0
+ R2: - C0 - C2 <= 0
+ R3: - C1 - C3 <= 0
+Bounds
+ C0 free
+ C1 free
+ C2 free
+ C3 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 x[0] + 0 x[1] + norm1_1 + 3 Constant
+Subject To
+Bounds
+ x[0] free
+ x[1] free
+ Constant = 1
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( x[0] , x[1] )
+End

tests/snapshots/all__lp_genexpr_norm1_11__0.txt

@@ -0,0 +1,36 @@
+CVXPY
+Maximize
+  Sum(x @ [ 1. -2.], None, False)
+Subject To
+ 40: norm1(x) <= 1.0
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  - C0 + 2 C1
+Subject To
+ R0: C0 - C2 <= 0
+ R1: C1 - C3 <= 0
+ R2: - C0 - C2 <= 0
+ R3: - C1 - C3 <= 0
+ R4: C2 + C3 <= 1
+Bounds
+ C0 free
+ C1 free
+ C2 free
+ C3 free
+End
+----------------------------------------
+GUROBI
+Maximize
+  x[0] - 2 x[1]
+Subject To
+ 40: norm1_1 <= 1
+Bounds
+ x[0] free
+ x[1] free
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( x[0] , x[1] )
+End

tests/snapshots/all__lp_genexpr_norm1_12__0.txt

@@ -0,0 +1,43 @@
+CVXPY
+Minimize
+  norm1(X)
+Subject To
+Bounds
+ X free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0 + C1 + C2 + C3
+Subject To
+ R0: - C0 + C4 <= 0
+ R1: - C1 + C5 <= 0
+ R2: - C2 + C6 <= 0
+ R3: - C3 + C7 <= 0
+ R4: - C0 - C4 <= 0
+ R5: - C1 - C5 <= 0
+ R6: - C2 - C6 <= 0
+ R7: - C3 - C7 <= 0
+Bounds
+ C0 free
+ C1 free
+ C2 free
+ C3 free
+ C4 free
+ C5 free
+ C6 free
+ C7 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 X[0,0] + 0 X[0,1] + 0 X[1,0] + 0 X[1,1] + norm1_1
+Subject To
+Bounds
+ X[0,0] free
+ X[0,1] free
+ X[1,0] free
+ X[1,1] free
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( X[0,0] , X[0,1] , X[1,0] , X[1,1] )
+End

tests/snapshots/all__lp_genexpr_norm1_13__0.txt

@@ -0,0 +1,53 @@
+CVXPY
+Minimize
+  norm1(X + -[[1.00 -2.00]
+ [3.00 -4.00]])
+Subject To
+Bounds
+ X free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0 + C1 + C2 + C3
+Subject To
+ R0: - C0 + C4 <= 1
+ R1: - C1 + C5 <= 3
+ R2: - C2 + C6 <= -2
+ R3: - C3 + C7 <= -4
+ R4: - C0 - C4 <= -1
+ R5: - C1 - C5 <= -3
+ R6: - C2 - C6 <= 2
+ R7: - C3 - C7 <= 4
+Bounds
+ C0 free
+ C1 free
+ C2 free
+ C3 free
+ C4 free
+ C5 free
+ C6 free
+ C7 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  norm1_2
+Subject To
+ R0: - X[0,0] + AddExpression_1[0,0] = -1
+ R1: - X[0,1] + AddExpression_1[0,1] = 2
+ R2: - X[1,0] + AddExpression_1[1,0] = -3
+ R3: - X[1,1] + AddExpression_1[1,1] = 4
+Bounds
+ X[0,0] free
+ X[0,1] free
+ X[1,0] free
+ X[1,1] free
+ AddExpression_1[0,0] free
+ AddExpression_1[0,1] free
+ AddExpression_1[1,0] free
+ AddExpression_1[1,1] free
+General Constraints
+ GC0: norm1_2 = NORM ( 1 ) ( AddExpression_1[0,0] , AddExpression_1[0,1] ,
+   AddExpression_1[1,0] , AddExpression_1[1,1] )
+End

tests/snapshots/all__lp_genexpr_norm1_14__0.txt

@@ -0,0 +1,45 @@
+CVXPY
+Minimize
+  norm1(X) + norm1([[1.00 -2.00]
+ [3.00 -4.00]])
+Subject To
+Bounds
+ X free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0 + C1 + C2 + C3
+Subject To
+ R0: - C0 + C4 <= 0
+ R1: - C1 + C5 <= 0
+ R2: - C2 + C6 <= 0
+ R3: - C3 + C7 <= 0
+ R4: - C0 - C4 <= 0
+ R5: - C1 - C5 <= 0
+ R6: - C2 - C6 <= 0
+ R7: - C3 - C7 <= 0
+Bounds
+ C0 free
+ C1 free
+ C2 free
+ C3 free
+ C4 free
+ C5 free
+ C6 free
+ C7 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 X[0,0] + 0 X[0,1] + 0 X[1,0] + 0 X[1,1] + norm1_1 + 10 Constant
+Subject To
+Bounds
+ X[0,0] free
+ X[0,1] free
+ X[1,0] free
+ X[1,1] free
+ Constant = 1
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( X[0,0] , X[0,1] , X[1,0] , X[1,1] )
+End

tests/snapshots/all__lp_genexpr_norm1_15__0.txt

@@ -0,0 +1,47 @@
+CVXPY
+Maximize
+  Sum(X @ [[1.00 -2.00]
+ [3.00 -4.00]], None, False)
+Subject To
+ 55: norm1(X) <= 1.0
+Bounds
+ X free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  - C0 - 3 C1 + 2 C2 + 4 C3
+Subject To
+ R0: C0 - C4 <= 0
+ R1: C1 - C5 <= 0
+ R2: C2 - C6 <= 0
+ R3: C3 - C7 <= 0
+ R4: - C0 - C4 <= 0
+ R5: - C1 - C5 <= 0
+ R6: - C2 - C6 <= 0
+ R7: - C3 - C7 <= 0
+ R8: C4 + C5 + C6 + C7 <= 1
+Bounds
+ C0 free
+ C1 free
+ C2 free
+ C3 free
+ C4 free
+ C5 free
+ C6 free
+ C7 free
+End
+----------------------------------------
+GUROBI
+Maximize
+  X[0,0] - 2 X[0,1] + 3 X[1,0] - 4 X[1,1]
+Subject To
+ 55: norm1_1 <= 1
+Bounds
+ X[0,0] free
+ X[0,1] free
+ X[1,0] free
+ X[1,1] free
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( X[0,0] , X[0,1] , X[1,0] , X[1,1] )
+End

tests/snapshots/all__lp_genexpr_norm1_1__0.txt

@@ -0,0 +1,30 @@
+CVXPY
+Minimize
+  norm1(x + -1.0)
+Subject To
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0
+Subject To
+ R0: - C0 + C1 <= 1
+ R1: - C0 - C1 <= -1
+Bounds
+ C0 free
+ C1 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  norm1_2
+Subject To
+ R0: - x + AddExpression_1 = -1
+Bounds
+ x free
+ AddExpression_1 free
+General Constraints
+ GC0: norm1_2 = NORM ( 1 ) ( AddExpression_1 )
+End

tests/snapshots/all__lp_genexpr_norm1_2__0.txt

@@ -0,0 +1,29 @@
+CVXPY
+Minimize
+  norm1(x) + norm1(-1.0)
+Subject To
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  C0
+Subject To
+ R0: - C0 + C1 <= 0
+ R1: - C0 - C1 <= 0
+Bounds
+ C0 free
+ C1 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 x + norm1_1 + Constant
+Subject To
+Bounds
+ x free
+ Constant = 1
+General Constraints
+ GC0: norm1_1 = NORM ( 1 ) ( x )
+End