diff --git a/src/booster/erlpboost/qp_model.rs b/src/booster/erlpboost/qp_model.rs
index ddcad08..49629d7 100644
--- a/src/booster/erlpboost/qp_model.rs
+++ b/src/booster/erlpboost/qp_model.rs
@@ -12,7 +12,7 @@ use crate::hypothesis::Classifier;
 
 use std::iter;
 
-const QP_TOLERANCE: f64 = 1e-300;
+const QP_TOLERANCE: f64 = 1e-9;
 
 /// A quadratic programming model for edge minimization. 
 /// `QPModel` solves the entropy regularized edge minimization problem:
@@ -45,33 +45,33 @@ const QP_TOLERANCE: f64 = 1e-300;
 /// ```txt
 /// # of   
 /// rows    γ        d1        ...     dm
-///       ┏    ┃                                 ┓   ┏   ┓
-///   1   ┃  0 ┃      1        ...      1        ┃ = ┃ 1 ┃
-///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
-///       ┃  0 ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃  0 ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃  . ┃     (-1) * Identity matrix      ┃ . ┃ . ┃
-///   m   ┃  . ┃              m x m              ┃ . ┃ . ┃
-///       ┃  . ┃                                 ┃ . ┃ . ┃
-///       ┃  0 ┃                                 ┃ ≤ ┃ 0 ┃
-///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
-///       ┃  0 ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃  0 ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃  . ┃                                 ┃ . ┃ . ┃
-///   m   ┃  . ┃         Identity matrix         ┃ . ┃ . ┃
-///       ┃  . ┃              m x m              ┃ . ┃ . ┃
-///       ┃  0 ┃                                 ┃ ≤ ┃ 0 ┃
-///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
-///       ┃ -1 ┃  y_1 h_1(x_1) ...  y_m h_1(x_m) ┃ ≤ ┃ 0 ┃
-///       ┃ -1 ┃  y_1 h_2(x_1) ...  y_m h_2(x_m) ┃ ≤ ┃ 0 ┃
-///       ┃  . ┃      .        ...      .        ┃ . ┃ . ┃
-///   H   ┃  . ┃      .        ...      .        ┃ . ┃ . ┃
-///       ┃  . ┃      .        ...      .        ┃ . ┃ . ┃
-///       ┃ -1 ┃  y_1 h_T(x_1) ...  y_m h_T(x_m) ┃ ≤ ┃ 0 ┃
-///       ┗    ┃                                 ┛   ┗   ┛
+///       ┏    ┃                                 ┓   ┏     ┓
+///   1   ┃  0 ┃      1        ...      1        ┃ = ┃  1  ┃
+///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+///       ┃  0 ┃                                 ┃ ≤ ┃  0  ┃
+///       ┃  0 ┃                                 ┃ ≤ ┃  0  ┃
+///       ┃  . ┃     (-1) * Identity matrix      ┃ . ┃  .  ┃
+///   m   ┃  . ┃              m x m              ┃ . ┃  .  ┃
+///       ┃  . ┃                                 ┃ . ┃  .  ┃
+///       ┃  0 ┃                                 ┃ ≤ ┃  0  ┃
+///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+///       ┃  0 ┃                                 ┃ ≤ ┃ 1/ν ┃
+///       ┃  0 ┃                                 ┃ ≤ ┃ 1/ν ┃
+///   m   ┃  . ┃         Identity matrix         ┃ . ┃  .  ┃
+///       ┃  . ┃              m x m              ┃ . ┃  .  ┃
+///       ┃  . ┃                                 ┃ . ┃  .  ┃
+///       ┃  0 ┃                                 ┃ ≤ ┃ 1/ν ┃
+///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+///       ┃ -1 ┃  y_1 h_1(x_1) ...  y_m h_1(x_m) ┃ ≤ ┃  0  ┃
+///       ┃ -1 ┃  y_1 h_2(x_1) ...  y_m h_2(x_m) ┃ ≤ ┃  0  ┃
+///       ┃  . ┃      .        ...      .        ┃ . ┃  .  ┃
+///   H   ┃  . ┃      .        ...      .        ┃ . ┃  .  ┃
+///       ┃  . ┃      .        ...      .        ┃ . ┃  .  ┃
+///       ┃ -1 ┃  y_1 h_T(x_1) ...  y_m h_T(x_m) ┃ ≤ ┃  0  ┃
+///       ┗    ┃                                 ┛   ┗     ┛
 ///
 /// # of
-/// cols     1 ┃               m
+/// cols    1 ┃               m
 /// ```
 pub(super) struct QPModel {
     pub(self) n_examples: usize,        // number of columns
@@ -124,7 +124,13 @@ impl QPModel {
         let rhs = self.build_rhs();
 
 
-        let mut old_objval = 1e9;
+        let mut old_objval = 1e3;
+
+        // Initialize `dist` as the uniform distribution.
+        dist.iter_mut()
+            .for_each(|di| {
+                *di = 1f64 / self.n_examples as f64;
+            });
         loop {
             let settings = DefaultSettingsBuilder::default()
                 .equilibrate_enable(true)
@@ -172,7 +178,7 @@ impl QPModel {
 
     pub(self) fn build_linear_part_objective(&self, dist: &[f64]) -> Vec<f64> {
         let mut linear = Vec::with_capacity(1 + self.n_examples);
-        linear.push(0f64);
+        linear.push(1f64);
         let iter = dist.into_iter()
             .copied()
             .map(|di| (1f64 / self.eta) * di.ln());
@@ -194,6 +200,9 @@ impl QPModel {
         col_ptr.push(0usize);
         row_val.push(0usize);
         nonzero.push(1f64);
+        // NOTE:
+        // we do not need to multiply 0.5f64 
+        // since clarabel add it automatically.
         for (i, &di) in (1..).zip(dist) {
             col_ptr.push(i);
             row_val.push(i);
@@ -238,7 +247,7 @@ impl QPModel {
 
             // capping constraint: `d_i ≤ 1/ν`
             row_val.push(self.n_examples + j);
-            nonzero.push(1f64);
+            nonzero.push(self.cap_inv);
 
             // margin constraints of `i`-th column
             for (i, &yh) in (0..).zip(margins) {
diff --git a/src/booster/softboost/qp_model.rs b/src/booster/softboost/qp_model.rs
index d30bdd7..7f9a8f6 100644
--- a/src/booster/softboost/qp_model.rs
+++ b/src/booster/softboost/qp_model.rs
@@ -47,30 +47,30 @@ const QP_TOLERANCE: f64 = 1e-9;
 /// ```txt
 /// # of   
 /// rows        d1        ...     dm
-///       ┏                                 ┓   ┏   ┓
-///   1   ┃      1        ...      1        ┃ = ┃ 1 ┃
-///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
-///       ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃     (-1) * Identity matrix      ┃ . ┃ . ┃
-///   m   ┃              m x m              ┃ . ┃ . ┃
-///       ┃                                 ┃ . ┃ . ┃
-///       ┃                                 ┃ ≤ ┃ 0 ┃
-///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
-///       ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃                                 ┃ ≤ ┃ 0 ┃
-///       ┃                                 ┃ . ┃ . ┃
-///   m   ┃         Identity matrix         ┃ . ┃ . ┃
-///       ┃              m x m              ┃ . ┃ . ┃
-///       ┃                                 ┃ ≤ ┃ 0 ┃
-///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
-///       ┃  y_1 h_1(x_1) ...  y_m h_1(x_m) ┃ ≤ ┃ 0 ┃
-///       ┃  y_1 h_2(x_1) ...  y_m h_2(x_m) ┃ ≤ ┃ 0 ┃
-///       ┃      .        ...      .        ┃ . ┃ . ┃
-///   H   ┃      .        ...      .        ┃ . ┃ . ┃
-///       ┃      .        ...      .        ┃ . ┃ . ┃
-///       ┃  y_1 h_T(x_1) ...  y_m h_T(x_m) ┃ ≤ ┃ 0 ┃
-///       ┗                                 ┛   ┗   ┛
+///       ┏                                 ┓   ┏     ┓
+///   1   ┃      1        ...      1        ┃ = ┃  1  ┃
+///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+///       ┃                                 ┃ ≤ ┃  0  ┃
+///       ┃                                 ┃ ≤ ┃  0  ┃
+///       ┃     (-1) * Identity matrix      ┃ . ┃  .  ┃
+///   m   ┃              m x m              ┃ . ┃  .  ┃
+///       ┃                                 ┃ . ┃  .  ┃
+///       ┃                                 ┃ ≤ ┃  0  ┃
+///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+///       ┃                                 ┃ ≤ ┃ 1/ν ┃
+///       ┃                                 ┃ ≤ ┃ 1/ν ┃
+///   m   ┃         Identity matrix         ┃ . ┃  .  ┃
+///       ┃              m x m              ┃ . ┃  .  ┃
+///       ┃                                 ┃ . ┃  .  ┃
+///       ┃                                 ┃ ≤ ┃ 1/ν ┃
+///      ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
+///       ┃  y_1 h_1(x_1) ...  y_m h_1(x_m) ┃ ≤ ┃  0  ┃
+///       ┃  y_1 h_2(x_1) ...  y_m h_2(x_m) ┃ ≤ ┃  0  ┃
+///       ┃      .        ...      .        ┃ . ┃  .  ┃
+///   H   ┃      .        ...      .        ┃ . ┃  .  ┃
+///       ┃      .        ...      .        ┃ . ┃  .  ┃
+///       ┃  y_1 h_T(x_1) ...  y_m h_T(x_m) ┃ ≤ ┃  0  ┃
+///       ┗                                 ┛   ┗     ┛
 ///
 /// # of
 /// cols                   m
@@ -236,7 +236,7 @@ impl QPModel {
 
             // capping constraint: `d_i ≤ 1/ν`
             row_val.push(self.n_examples + j + 1);
-            nonzero.push(1f64);
+            nonzero.push(self.cap_inv);
 
             // margin constraints of `i`-th column
             for (i, &yh) in (0..).zip(margins) {