scikit-learn · OmarManzoor · Sep 5, 2025 · Aug 21, 2025 · Aug 21, 2025 · Aug 21, 2025
diff --git a/doc/modules/linear_model.rst b/doc/modules/linear_model.rst
@@ -319,12 +319,14 @@ It stops if the duality gap is smaller than the provided tolerance `tol`.
 
   The duality gap :math:`G(w, v)` is an upper bound of the difference between the
   current primal objective function of the Lasso, :math:`P(w)`, and its minimum
-  :math:`P(w^\star)`, i.e. :math:`G(w, v) \leq P(w) - P(w^\star)`. It is given by
+  :math:`P(w^\star)`, i.e. :math:`G(w, v) \geq P(w) - P(w^\star)`. It is given by
   :math:`G(w, v) = P(w) - D(v)` with dual objective function
 
   .. math:: D(v) = \frac{1}{2n_{\text{samples}}}(y^Tv - ||v||_2^2)
 
   subject to :math:`v \in ||X^Tv||_{\infty} \leq n_{\text{samples}}\alpha`.
+  At optimum, the duality gap is zero, :math:`G(w^\star, v^\star) = 0` (a property
+  called strong duality).
   With (scaled) dual variable :math:`v = c r`, current residual :math:`r = y - Xw` and
   dual scaling
 

diff --git a/...sklearn.linear_model/31882.efficiency.rst → ...sklearn.linear_model/31986.efficiency.rst b/...sklearn.linear_model/31882.efficiency.rst → ...sklearn.linear_model/31986.efficiency.rst
@@ -1,11 +1,12 @@
 - :class:`linear_model.ElasticNet`, :class:`linear_model.ElasticNetCV`,
   :class:`linear_model.Lasso`, :class:`linear_model.LassoCV` as well as
   :func:`linear_model.lasso_path` and :func:`linear_model.enet_path` now implement
-  gap safe screening rules in the coordinate descent solver for dense `X` and
-  `precompute=False` or `"auto"` with `n_samples < n_features`.
+  gap safe screening rules in the coordinate descent solver for dense `X` (with
+  `precompute=False` or `"auto"` with `n_samples < n_features`) and sparse `X`
+  (always).
   The speedup of fitting time is particularly pronounced (10-times is possible) when
   computing regularization paths like the \*CV-variants of the above estimators do.
   There is now an additional check of the stopping criterion before entering the main
   loop of descent steps. As the stopping criterion requires the computation of the dual
   gap, the screening happens whenever the dual gap is computed.
-  By :user:`Christian Lorentzen <lorentzenchr>`.
+  By :user:`Christian Lorentzen <lorentzenchr>` :pr:`31882` and