diff --git a/src/raking/loss_functions.py b/src/raking/loss_functions.py
new file mode 100644
index 0000000..f202428
--- /dev/null
+++ b/src/raking/loss_functions.py
@@ -0,0 +1,27 @@
+"""This module contains loss functions with their gradient and hessian"""
+
+import numpy as np
+
+def compute_loss(beta, C, c, loss):
+    """
+    """
+    x = c - np.matmul(C, beta)
+    if loss == 'hinge':
+        loss_val = np.sum(np.power(np.maximum(0.0, -x), 3.0))
+        loss_grad = - 3.0 * np.square(np.maximum(0.0, -x))
+        loss_hess = np.diag(6.0 * np.maximum(0, -x))
+    if loss == 'logit':
+        loss_val = np.sum(np.log(1.0 + np.exp(-x)))
+        loss_grad = - np.exp(-x) / (1.0 + np.exp(-x))
+        loss_hess = np.diag(np.exp(-x) / np.square(1.0 + np.exp(-x)))
+    return (loss_val, loss_grad, loss_hess)
+
+def compute_dist(beta, y, q, method):
+    """
+    """
+    if method == 'chi2':
+        dist_val = np.sum(np.square(beta - y) / (2.0 * q * y))
+        dist_grad = (beta / y - 1.0) / q
+        dist_hess = np.diag(1.0 / (q * y))
+    return (dist_val, dist_grad, dist_hess)
+
diff --git a/src/raking/raking_loss.py b/src/raking/raking_loss.py
new file mode 100644
index 0000000..0cbb6ec
--- /dev/null
+++ b/src/raking/raking_loss.py
@@ -0,0 +1,50 @@
+"""Module with methods to solve the raking problem with a penalty loss"""
+
+import numpy as np
+
+from scipy.sparse.linalg import cg
+
+from loss_functions import compute_loss, compute_dist
+
+def raking_chi2_loss(
+    y: np.ndarray,
+    A: np.ndarray,
+    s: np.ndarray,
+    C: np.ndarray,
+    c: np.ndarray,
+    q: np.ndarray,
+    method: str = 'chi2',
+    loss: str = 'logit',
+    penalty: float = 1.0,
+    gamma0: float = 1.0,
+    max_iter: int = 500,
+):
+    """
+    """
+    beta = np.copy(y)
+    lambda_k = np.zeros(A.shape[0])
+    sol_k = np.concatenate((beta, lambda_k))
+    epsilon = 1.0
+    iter_eps = 0
+    while (epsilon > 1.0e-10) & (iter_eps < max_iter):
+        (loss_val, loss_grad, loss_hess) = compute_loss(beta, C, c, loss)
+        (dist_val, dist_grad, dist_hess) = compute_dist(beta, y, q, method)
+        F1 = dist_grad + np.matmul(np.transpose(A), lambda_k) \
+            - penalty * np.matmul(np.transpose(C), loss_grad)
+        F2 = np.matmul(A, beta) - s
+        F = np.concatenate((F1, F2))
+        J = dist_hess + penalty * np.matmul(np.transpose(C), np.matmul(loss_hess, C))
+        J = np.concatenate(
+            (np.concatenate((J, np.transpose(A)), axis=1),
+             np.concatenate((A, np.zeros((A.shape[0], A.shape[0]))), axis=1),
+            ), axis=0,
+        )
+        delta_sol = cg(J, F)[0]
+        sol_k = sol_k - delta_sol
+        beta = sol_k[0:A.shape[1]]
+        lambda_k = sol_k[A.shape[1]:(A.shape[0] + A.shape[1])]
+        epsilon = np.mean(np.abs(s - np.matmul(A, beta)))
+        iter_eps = iter_eps + 1
+        print(iter_eps, epsilon, dist_val, loss_val)
+    return (beta, lambda_k, iter_eps)
+