# Forward-backward truncated Newton methods for convex composite optimization

arXiv: https://arxiv.org/abs/1402.6655 · HTML: https://mlsanity.com/paper/1402.6655/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2014.

## Built on by (most cited first, 3 of 3)

- [SCORE: Approximating Curvature Information under Self-Concordant Regularization](https://mlsanity.com/paper/2112.07344/) (2021)
- [Accelerated forward-backward and Douglas-Rachford splitting dynamics](https://mlsanity.com/paper/2407.20620/) (2024)
- [Self-concordant smoothing in proximal quasi-Newton algorithms for large-scale convex composite optimization](https://mlsanity.com/paper/2309.01781/) (2023)

## Abstract (arXiv)

This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the second one combines the global efficiency estimates of the corresponding first-order methods, while achieving fast asymptotic convergence rates. Furthermore, they are computationally attractive since each Newton iteration requires the approximate solution of a linear system of usually small dimension.