AugmentedMixing

AugmentedMixing.jl is a Julia implementation of the Augmented Mixing Method for solving general large-scale SDPs of the form

$$\begin{array}{rl} \text{minimize} \quad & \displaystyle \sum_{i=1}^q \langle C_i, X_i \rangle \\[1.2ex] \text{subject to} \quad & \displaystyle \sum_{i=1}^q \mathcal{A}_i(X_i) = a, \\\\\ & \displaystyle \sum_{i=1}^q \mathcal{B}_i(X_i) \geq b, \\\\\ & X_i \in \mathcal{S}_+^{n_i}, \quad i = 1,\ldots, q. \end{array}$$

This method features a Burer-Monteiro factorization-based algorithm in which all factorization matrices are updated in a column-wise fashion and is in particular designed to handle a large number of inequality constraints.

Installation

This package is not yet registered in the Julia General registry. You can install the latest version directly from GitHub:

using Pkg
Pkg.add(url="https://github.com/jschwiddessen/AugmentedMixing.jl.git")

References

This package is based on the preprint

Daniel Brosch, Jan Schwiddessen, Angelika Wiegele. (2025). The Augmented Mixing Method: Computing High-Accuracy Primal-Dual Solutions to Large-Scale SDPs via Column Updates. [Manuscript submitted for publication].

Citation

If you use this package in your academic work, please cite the following:

@misc{brosch2025augmented,
      title={The Augmented Mixing Method: Computing High-Accuracy Primal-Dual Solutions to Large-Scale SDPs via Column Updates}, 
      author={Daniel Brosch and Jan Schwiddessen and Angelika Wiegele},
      year={2025},
      eprint={2507.20386},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/2507.20386}, 
}