Adopt three-way atom classification: smooth, nonsmooth-convex, nonsmooth-concave

Replace the two-axis is_atom_linearizable_convex/concave overrides across all
atoms with a single method from the paper's three categories: is_atom_smooth,
is_atom_nonsmooth_convex, or is_atom_nonsmooth_concave. The base class derives
the old linearizable methods for backward compatibility.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: Transurgeon

CLAUDE.md

@@ -176,9 +176,23 @@ The diff engine supports CVXPY `Parameter` objects: `C_problem` registers parame
 1. Create a canonicalizer in `cvxpy/reductions/dnlp2smooth/canonicalizers/`
 2. The canonicalizer converts non-smooth atoms to smooth equivalents using auxiliary variables
 3. Register in `canonicalizers/__init__.py` by adding to `SMOOTH_CANON_METHODS` dict
-4. Ensure the atom has proper `is_smooth()`, `is_linearizable_convex()`, `is_linearizable_concave()` methods
+4. Classify the atom using the three-way atom-level API (see below)
 
-### DNLP Rules (Linearizable Convex / Linearizable Concave)
+### DNLP Atom Classification (Three-way)
+
+Each atom implements exactly one of three atom-level methods:
+
+| Category | Method | Examples |
+|---|---|---|
+| **Smooth** | `is_atom_smooth() → True` | exp, log, power, sin, prod, quad_form |
+| **NS-convex** | `is_atom_nonsmooth_convex() → True` | abs, max, norm1, norm_inf, huber |
+| **NS-concave** | `is_atom_nonsmooth_concave() → True` | min, minimum |
+
+The base class in `atom.py` derives backward-compatible convenience methods:
+- `is_atom_linearizable_convex()` = `is_atom_smooth() or is_atom_nonsmooth_convex()`
+- `is_atom_linearizable_concave()` = `is_atom_smooth() or is_atom_nonsmooth_concave()`
+
+### DNLP Expression-level Rules
 
 - **Smooth**: functions that are both linearizable convex and linearizable concave (analogous to affine in DCP)
 - **Linearizable Convex**: can be minimized or appear in `<= 0` constraints

cvxpy/atoms/affine/affine_atom.py

@@ -57,14 +57,8 @@ def is_atom_concave(self) -> bool:
         """
         return True
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_incr(self, idx) -> bool:

cvxpy/atoms/atom.py

@@ -188,17 +188,25 @@ def is_atom_affine(self) -> bool:
         """
         return self.is_atom_concave() and self.is_atom_convex()
 
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth (infinitely differentiable)?"""
+        return False
+
+    def is_atom_nonsmooth_convex(self) -> bool:
+        """Is the atom nonsmooth and convex?"""
+        return False
+
+    def is_atom_nonsmooth_concave(self) -> bool:
+        """Is the atom nonsmooth and concave?"""
+        return False
+
     def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        raise NotImplementedError("is_atom_linearizable_convex not implemented for %s."
-                                   % self.__class__.__name__)
-    
+        """Is the atom convex after linearizing?"""
+        return self.is_atom_smooth() or self.is_atom_nonsmooth_convex()
+
     def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
-        raise NotImplementedError("is_atom_linearizable_concave not implemented for %s."
-                                   % self.__class__.__name__)
+        """Is the atom concave after linearizing?"""
+        return self.is_atom_smooth() or self.is_atom_nonsmooth_concave()
 
     def is_atom_log_log_convex(self) -> bool:
         """Is the atom log-log convex?

cvxpy/atoms/elementwise/abs.py

@@ -56,16 +56,10 @@ def is_atom_concave(self) -> bool:
         """
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
+    def is_atom_nonsmooth_convex(self) -> bool:
+        """Is the atom nonsmooth and convex?"""
         return True
 
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
-        return False
-
     def is_incr(self, idx) -> bool:
         """Is the composition non-decreasing in argument idx?
         """

cvxpy/atoms/elementwise/entr.py

@@ -58,14 +58,8 @@ def is_atom_concave(self) -> bool:
         """
         return True
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_incr(self, idx) -> bool:

cvxpy/atoms/elementwise/exp.py

@@ -55,14 +55,8 @@ def is_atom_concave(self) -> bool:
         """
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_atom_log_log_convex(self) -> bool:

cvxpy/atoms/elementwise/huber.py

@@ -71,16 +71,10 @@ def is_atom_concave(self) -> bool:
         """Is the atom concave?"""
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
+    def is_atom_nonsmooth_convex(self) -> bool:
+        """Is the atom nonsmooth and convex?"""
         return True
 
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
-        return False
-
     def is_incr(self, idx) -> bool:
         """Is the composition non-decreasing in argument idx?"""
         return self.args[idx].is_nonneg()

cvxpy/atoms/elementwise/hyperbolic.py

@@ -50,14 +50,8 @@ def is_atom_concave(self) -> bool:
         """
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_incr(self, idx) -> bool:
@@ -74,7 +68,7 @@ def _domain(self) -> List[Constraint]:
         """Returns constraints describing the domain of the node.
         """
         return []
-    
+
     def _grad(self, values) -> List[Constraint]:
         raise NotImplementedError("Gradient not implemented for sinh.")
 
@@ -107,15 +101,9 @@ def is_atom_concave(self) -> bool:
         """Is the atom concave?
         """
         return False
-    
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
 
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_incr(self, idx) -> bool:
@@ -160,10 +148,7 @@ def is_atom_convex(self) -> bool:
     def is_atom_concave(self) -> bool:
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
+    def is_atom_smooth(self) -> bool:
         return True
 
     def is_incr(self, idx) -> bool:
@@ -202,10 +187,7 @@ def is_atom_convex(self) -> bool:
     def is_atom_concave(self) -> bool:
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
+    def is_atom_smooth(self) -> bool:
         return True
 
     def is_incr(self, idx) -> bool:

cvxpy/atoms/elementwise/kl_div.py

@@ -55,14 +55,8 @@ def is_atom_concave(self) -> bool:
         """
         return False
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_incr(self, idx) -> bool:

cvxpy/atoms/elementwise/log.py

@@ -56,14 +56,8 @@ def is_atom_concave(self) -> bool:
         """
         return True
 
-    def is_atom_linearizable_convex(self) -> bool:
-        """Is the atom convex after linearizing?
-        """
-        return True
-
-    def is_atom_linearizable_concave(self) -> bool:
-        """Is the atom concave after linearizing?
-        """
+    def is_atom_smooth(self) -> bool:
+        """Is the atom smooth?"""
         return True
 
     def is_atom_log_log_convex(self) -> bool: