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Gradient Descent

Minimize f(x) using gradient descent (1D or 2D).

Input
Result

Enter function.

Technical Description & Theory

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.