# Entropy Penalized Semidefinite Programming

arXiv: https://arxiv.org/abs/1802.04332 · HTML: https://mlsanity.com/paper/1802.04332/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

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

- [Large-Scale Sequential Learning for Recommender and Engineering Systems](https://mlsanity.com/paper/2205.06893/) (2022)
- [Inference and Optimization for Engineering and Physical Systems](https://mlsanity.com/paper/2208.13880/) (2022)
- [Data-Driven Stochastic AC-OPF using Gaussian Processes](https://mlsanity.com/paper/2402.11365/) (2024)

## Abstract (arXiv)

Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement in practice due to high computational efforts. In this paper, we propose Entropy Penalized Semi-definite programming (EP-SDP) which provides a unified framework for a wide class of penalty functions used in practice to promote a low-rank solution. We show that EP-SDP problems admit efficient numerical algorithm having (almost) linear time complexity of the gradient iteration which makes it useful for many machine learning and optimization problems. We illustrate the practical efficiency of our approach on several combinatorial optimization and machine learning problems.