diff --git a/project_euromir/loss_nullspace_proj.py b/project_euromir/loss_nullspace_proj.py
new file mode 100644
index 0000000..ca194f4
--- /dev/null
+++ b/project_euromir/loss_nullspace_proj.py
@@ -0,0 +1,35 @@
+"""Loss and related functions for nullspace projection model."""
+
+import numpy as np
+
+
+class NullSpaceModel:
+
+    def __init__(
+        self, m, n, zero, nonneg, matrix_transfqr, b, c, nullspace_projector):
+        self.m = m
+        self.n = n
+        self.zero = zero
+        self.nonneg = nonneg
+        self.matrix = matrix_transfqr,
+        self.b = b
+        self.c = c
+        self.nullspace_projector = nullspace_projector
+
+        # since matrix is from QR
+        self.y0 = -self.c @ self.matrix.T
+
+    def loss(self, variable):
+        x = variable[:self.n]; y_null = variable[self.n:]
+        y = self.y0 + self.nullspace_projector @ y_null
+        s = -self.matrix @ x + self.b
+        y_loss = np.linalg.norm(np.minimum(y[self.zero:], 0.))**2
+        s_loss_zero = np.linalg.norm(s[:self.zero])**2
+        s_loss_nonneg = np.linalg.norm(np.minimum(s[self.zero:], 0.))**2
+        gap_loss = (self.c.T @ x + self.b.T @ y)**2
+        return (y_loss + s_loss_zero + s_loss_nonneg + gap_loss) / 2.
+
+    def gradient(self, variable):
+        x = variable[:self.n]; y_null = variable[self.n:]
+        y = self.y0 + self.nullspace_projector @ y_null
+        s = -self.matrix @ x + self.b