# Adaptive Catalyst for Smooth Convex Optimization

arXiv: https://arxiv.org/abs/1911.11271 · HTML: https://mlsanity.com/paper/1911.11271/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

## Built on by (most cited first, 6 of 6)

- [RECAPP: Crafting a More Efficient Catalyst for Convex Optimization](https://mlsanity.com/paper/2206.08627/) (2022)
- [Stabilized Proximal-Point Methods for Federated Optimization](https://mlsanity.com/paper/2407.07084/) (2024)
- [Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penalties](https://mlsanity.com/paper/2211.14645/) (2022)
- [Smooth Quasar-Convex Optimization with Constraints](https://mlsanity.com/paper/2510.01943/) (2025)
- [Complexity of Inexact Proximal Point Algorithm for minimizing convex functions with Holderian Growth](https://mlsanity.com/paper/2108.04482/) (2021)
- [An Optimal Algorithm for Strongly Convex Min-min Optimization](https://mlsanity.com/paper/2212.14439/) (2022)

## Abstract (arXiv)

In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in Catalyst (Lin et al., 2015): an accelerated proximal outer gradient method, which is used as an envelope for a non-accelerated inner method for the ℓ2 regularized auxiliary problem. Our algorithm has two key differences: 1) easily verifiable stopping criteria for inner algorithm; 2) the regularization parameter can be tunned along the way. As a result, the main contribution of our work is a new framework that applies to adaptive inner algorithms: Steepest Descent, Adaptive Coordinate Descent, Alternating Minimization. Moreover, in the non-adaptive case, our approach allows obtaining Catalyst without a logarithmic factor, which appears in the standard Catalyst (Lin et al., 2015, 2018).