# Contracting Proximal Methods for Smooth Convex Optimization

arXiv: https://arxiv.org/abs/1912.07972 · HTML: https://mlsanity.com/paper/1912.07972/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Super-Universal Regularized Newton Method](https://mlsanity.com/paper/2208.05888/) (2022)
- [Minimizing Quasi-Self-Concordant Functions by Gradient Regularization of Newton Method](https://mlsanity.com/paper/2308.14742/) (2023)
- [Stabilized Proximal-Point Methods for Federated Optimization](https://mlsanity.com/paper/2407.07084/) (2024)
- [Primal Acceleration of Newton's Method](https://mlsanity.com/paper/2608.21359/) (2026)

## Abstract (arXiv)

In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a regularization term in the form of Bregman divergence. We provide global convergence analysis for a general scheme admitting inexactness in solving the auxiliary subproblem. In the case of using for this purpose high-order tensor methods, we demonstrate an acceleration effect for both convex and uniformly convex composite objective functions. Thus, our construction explains acceleration for methods of any order starting from one. The augmentation of the number of calls of oracle due to computing the contracted proximal steps is limited by the logarithmic factor in the worst-case complexity bound.