```markdown
### Implementation

Main effort in each iteration: evaluate derivatives and solve Newton system

\[ H \Delta x = g \]

where \( H = \nabla^2 f(x) \), \( g = -\nabla f(x) \)

#### Via Cholesky factorization

\[ H = LL^T, \quad \Delta x_{nt} = L^{-T}L^{-1}g, \quad \lambda(x) = \|L^{-1}g\|_2 \]

- Cost \((1/3)n^3\) flops for unstructured system
- Cost \(\ll (1/3)n^3\) if \( H \) sparse, banded

*Source: A. d’Aspremont. Convex Optimization M2.*
```