SuperADMM

Fast Quadratic Program Solver with dynamic weighting ADMM

This algorithm specifically solves problems of shape

$$ \begin{equation} \begin{aligned} & \underset{x}{\textbf{minimize}} & & \tfrac12 x^\top P x + x^\top q\ & \textbf{subject to} & & l \le Ax \le u \ \end{aligned} \end{equation} $$

where $x \in \mathrm{R}^n$ is the optimization variable, $P \in \mathrm{R}^{n \times n}$ and $q \in \mathrm{R}^n$ describe the quadratic cost function ($P$ is positive semi-definite), $A \in \mathrm{R}^{m \times n}$ is the linear constraint mapping and $l \in\mathrm{R}^m$, $u\in\mathrm{R}^m$ denote the lower and upper bounds of the constraints. Note that by setting $l_i = u_i$ for some index $i$, one can also include equality constraints in the problem. Furthermore, $l_i = -\infty$ or $u_i = \infty$ allows users to only consider lower or upper bounds.

Installation

Installation is currently only available in Windows, Linux and MACOS will follow later

Python

At this moment, we are working on changing this install routine to pip install superADMM, but as of now, that is yet unavailable. Instead, this should be the correct (and very cumbersome) install procedure.

• Download or clone this package
• Download and unpack OpenBLAS binaries (OpenBLAS-x.x.xx_x64.zip): https://github.com/OpenMathLib/OpenBLAS/releases
• In setup.py, change openblas_include and openblas_lib to the folder path where you unpacked OpenBLAS.
• Open Command Prompt at the superADMM folder (that is, the main, not superADMM/superADMM)
• python -m build --wheel (this will throw a bunch of warnings, which is fine. However, it can give some errors that some packages might need to be installed, install them if so)
• pip install dist\superadmm-0.7.0-cpVERSION-cpVERSION-win_amd64.whl, where VERSION is your python version (for me it says cp313). You can find the .whl file in the dist folder to check the correct name.
• Enjoy your fast solver in Python with import superADMM

MATLAB (Express installation)

• Download the latest release (https://github.com/Petrus1904/superADMM/releases)
• Unzip the contents in some folder
• Run superADMM_setup.m
• Enjoy your fast solver in MATLAB with superADMM.m

MATLAB (Manual installation)

• Download or clone this package
• Ensure that MATLAB mex add-on (code-generation) is installed, and gcc (MinGW64) is installed as mex compiler
• Verify with mex -setup that MinGW64 is the default compiler
• Run compile.m
• Enjoy your fast solver in MATLAB with superADMM.m

How to Cite

APA:

Verheijen, P.C.N., Goswami, D., and Lazar, M. (2025). SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM. arXiv: 2506.11608 [math.OC]. URL: https://arxiv.org/abs/2506.11608

Bibtex:

@misc{superADMM:Verheijen2025,
      title={{SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM}}, 
      author={P. C. N. Verheijen and D. Goswami and M. Lazar},
      year={2025},
      eprint={2506.11608},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/2506.11608}, 
}

References

The fast execution of various linear algebraic operations is provided by a set of third party libraries, which we list below:

• [OpenBLAS] Wang Qian, Zhang Xianyi, Zhang Yunquan, Qing Yi, AUGEM: Automatically Generate High Performance Dense Linear Algebra Kernels on x86 CPUs, In the International Conference for High Performance Computing, Networking, Storage and Analysis (SC'13), Denver CO, November 2013
• [LAPACK] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, 3rd e. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1999.
• [CSPARSE] T.A. Davis, Direct Methods for Sparse Linear Systems. SIAM, 2006
• [LDL] T.A. Davis, Algorithm 849: A concise sparse cholesky factorization package, ACM Trans. Math. Softw. vol. 31, no. 4, p. 587-591, Dec. 2005

License

SuperADMM is licensed under LGPL 2.1.