Gradient Descent

Interactive optimization of mathematical functions

Speed:

Learning Rate: 0.1

Max Iterations: 100

Initial x: 4

Function: x²

Current Position

Optimization Path

Tangent (Derivative)

Step Direction

Algorithm: xₙ₊₁ = xₙ - α·∇f(xₙ)

Goal: Find x that minimizes f(x)

Learning Rate (α): Step size

Convergence: When |∇f(x)| < threshold

Challenges:

• Local minima

• Learning rate too large/small

• Saddle points