# Composite Self-Concordant Minimization

arXiv: https://arxiv.org/abs/1308.2867 · HTML: https://mlsanity.com/paper/1308.2867/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2013.

## Built on by (most cited first, 8 of 8)

- [Near-Optimal No-Regret Learning Dynamics for General Convex Games](https://mlsanity.com/paper/2206.08742/) (2022)
- [Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography](https://mlsanity.com/paper/2211.12880/) (2022)
- [Gradient Descent-Type Methods: Background and Simple Unified Convergence Analysis](https://mlsanity.com/paper/2212.09413/) (2022)
- [Self-concordant smoothing in proximal quasi-Newton algorithms for large-scale convex composite optimization](https://mlsanity.com/paper/2309.01781/) (2023)
- [Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging](https://mlsanity.com/paper/2311.02557/) (2023)
- [Efficient proximal gradient algorithms for joint graphical lasso](https://mlsanity.com/paper/2107.07799/) (2021)
- [NewVEM: A Newton Vertex Exchange Method for a Class of Constrained Self-Concordant Minimization Problems](https://mlsanity.com/paper/2407.03294/) (2024)
- [An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2607.13919/) (2026)

## Abstract (arXiv)

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size selection and correction procedures based on the structure of the problem. We describe concrete algorithmic instances of our framework for several interesting applications and demonstrate them numerically on both synthetic and real data.