# A User Manual for cuHALLaR: A GPU Accelerated Low-Rank Semidefinite Programming Solver

arXiv: https://arxiv.org/abs/2508.15951 · HTML: https://mlsanity.com/paper/2508.15951/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs](https://mlsanity.com/paper/1802.03504/) (2018)
- [A low-rank augmented Lagrangian method for large-scale semidefinite programming based on a hybrid convex-nonconvex approach](https://mlsanity.com/paper/2401.12490/) (2024)
- [An adaptive superfast inexact proximal augmented Lagrangian method for smooth nonconvex composite optimization problems](https://mlsanity.com/paper/2207.11905/) (2022)
- [An efficient adaptive accelerated inexact proximal point method for solving linearly constrained nonconvex composite problems](https://mlsanity.com/paper/1812.06352/) (2018)
- [cuHALLaR: A GPU Accelerated Low-Rank Augmented Lagrangian Method for Large-Scale Semidefinite Programming](https://mlsanity.com/paper/2505.13719/) (2025)

## Abstract (arXiv)

We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with SDPA and a new enhanced data format taking advantage of Hybrid Sparse Low-Rank (HSLR) structure. The interface allows users to load custom data files, configure solver options, and execute experiments directly from Julia. A collection of example problems is included, including the SDP relaxations of the Matrix Completion and Maximum Stable Set problems.