diff --git a/cyanure/estimators.py b/cyanure/estimators.py
index 174468976..743adb0bf 100644
--- a/cyanure/estimators.py
+++ b/cyanure/estimators.py
@@ -1,7 +1,6 @@
 """Contain the different estimators of the library."""
 
 from abc import abstractmethod, ABC
-
 import math
 import inspect
 import warnings
@@ -50,6 +49,9 @@ def _warm_start(self, X, initial_weight, nclasses):
             else:
                 initial_weight = np.squeeze(self.coef_)
 
+
+        initial_weight = np.asfortranarray(initial_weight, X.dtype)
+
         if self.warm_start and self.solver in ('auto', 'miso', 'catalyst-miso', 'qning-miso'):
             n = X.shape[0]
             # TODO Ecrire test pour dual surtout défensif
@@ -286,17 +288,19 @@ def fit(self, X, labels, le_parameter=None):
 
         if (self.multi_class == "multinomial" or
            (self.multi_class == "auto" and not self._binary_problem)) and self.loss == "logistic":
-            if self.multi_class == "multinomial":
-                if len(np.unique(labels)) != 2:
-                    self._binary_problem = False
+            if len(np.unique(labels)) != 2:
+                self._binary_problem = False
 
-            loss = "multiclass-logistic"
-            logger.info(
-                "Loss has been set to multiclass-logistic because "
-                "the multiclass parameter is set to multinomial!")
+                loss = "multiclass-logistic"
+                logger.info(
+                    "Loss has been set to multiclass-logistic because "
+                    "the multiclass parameter is set to multinomial!")
 
         if loss is None:
             loss = self.loss
+        
+        if (loss == "multiclass-logistic" or loss == "logistic") and self.lambda_1 == 1.0:
+            self.lambda_1 = 1 / len(X)
 
         labels = np.squeeze(labels)
         initial_weight, yf, nclasses = self._initialize_weight(X, labels)
@@ -1175,7 +1179,7 @@ class LogisticRegression(Classifier):
     _estimator_type = "classifier"
 
     def __init__(self, penalty='l2', loss='logistic', fit_intercept=True,
-                 verbose=False, lambda_1=0, lambda_2=0, lambda_3=0,
+                 verbose=False, lambda_1=1.0, lambda_2=0, lambda_3=0,
                  solver='auto', tol=1e-3, duality_gap_interval=10,
                  max_iter=500, limited_memory_qning=20,
                  fista_restart=50, warm_start=False, n_threads=-1,