Function levenbergMarquardt

Performs Levenberg-Marquardt optimization for nonlinear least squares problems.

Algorithm:

1. Start with initial parameters and lambda (damping parameter)
2. Compute residual vector r and Jacobian matrix J
3. Solve damped normal equations: (J^T J + λI) δ = -J^T r
4. Try step: x_new = x_old + δ
5. If cost decreases: accept step, decrease lambda
6. If cost increases: reject step, increase lambda
7. Repeat until convergence

The damping parameter lambda interpolates between:

• Gauss-Newton (λ → 0): fast convergence near solution
• Gradient descent (λ → ∞): robust but slow