Create app.py

app.py

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+# Convex vs Non-Convex Optimization Demo (Colab-ready)
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Define convex and non-convex functions
+def convex_fn(x): return x**2
+def nonconvex_fn(x): return x**4 - 3*x**3 + 2
+
+# Gradient functions
+def grad_convex(x): return 2*x
+def grad_nonconvex(x): return 4*x**3 - 9*x**2
+
+# Gradient descent
+def gradient_descent(f, grad_f, x0, lr=0.01, steps=50):
+    x_vals, y_vals = [x0], [f(x0)]
+    x = x0
+    for _ in range(steps):
+        x -= lr * grad_f(x)
+        x_vals.append(x)
+        y_vals.append(f(x))
+    return x_vals, y_vals
+
+# Run optimization
+x_c, y_c = gradient_descent(convex_fn, grad_convex, x0=5)
+x_nc, y_nc = gradient_descent(nonconvex_fn, grad_nonconvex, x0=2)
+
+# Plotting
+fig, axs = plt.subplots(1, 2, figsize=(12, 4))
+x = np.linspace(-1, 6, 100)
+
+axs[0].plot(x, convex_fn(x), label='Convex Function')
+axs[0].scatter(x_c, y_c, c='red', s=10, label='Gradient Descent Path')
+axs[0].set_title('Convex Optimization')
+axs[0].legend()
+
+axs[1].plot(x, nonconvex_fn(x), label='Non-Convex Function')
+axs[1].scatter(x_nc, y_nc, c='purple', s=10, label='Gradient Descent Path')
+axs[1].set_title('Non-Convex Optimization')
+axs[1].legend()
+
+plt.tight_layout()
+plt.show()