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utils/backtracking.py

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+import numpy as np
+
+def backtracking(f, grad_f, x):
+    """
+    This function is a simple implementation of the backtracking algorithm for
+    the GD (Gradient Descent) method.
+    
+    f: function. The function that we want to optimize.
+    grad_f: function. The gradient of f(x).
+    x: ndarray. The actual iterate x_k.
+    """
+    alpha = 1
+    c = 0.8
+    tau = 0.25
+
+    while f(x - alpha * grad_f(x)) > f(x) - c * alpha * np.linalg.norm(grad_f(x), 2) ** 2:
+        alpha = tau * alpha
+
+        if alpha < 1e-5:
+            break
+
+    return alpha