What is Nonlinear Optimization Gradient Descent Calculator and Why it Matters?
Gradient descent is the fundamental iterative method for unconstrained minimization and underpins modern machine-learning training.
Mathematical Formula and Theory
x_{k+1} = x_k − η ∇f(x_k). For smooth functions and small η the sequence converges to a stationary point.
How to Use This Calculator - Step by Step
- Enter f(x) or f(x,y), starting point, learning rate, and iterations.
- Click Minimize.
Solved Example with Full Calculation
Minimize (x−2)²+(y−3)² from (0,0) with η=0.1 reaches approximately (2,3), the exact minimizer.