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CaΣoS provides tools for symbolic polynomial expressions, conic optimization, and parametrized (convex and nonconvex) sum-of-squares optimization, making use of the CasADi software for symbolic expressions, automatic differentiation, and numerical optimization. CaΣoS is developed by researchers at the Institute of Flight Mechanics and Controls of the University of Stuttgart and distributed open-source under the GPL-3.0 license.

Downloads

• All platforms: Stable version 1.0.1
• CaΣoS example package
• Reference values for unit tests

Quick links

• Install latest version
• Available conic solvers
• Convex and nonconvex sum-of-squares optimization
• Supported vector, matrix, and polynomial cones
• Some practical tipps to sum-of-squares
• Transitioning from other toolboxes
• Example code snippets

Publications

If you use CaΣoS, please cite us:

1. T. Cunis and J. Olucak, ‘CaΣoS: A nonlinear sum-of-squares optimization suite’, in 2025 American Control Conference, (Denver, CO), pp. 1659–1666, 2025. doi: 10.23919/ACC63710.2025.11107794

2. J. Olucak and T. Cunis, ‘On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems’, Pre-print. arXiv: 2602.02394

Bibtex entry

@inproceedings{Cunis2025acc,
	author = {Cunis, Torbjørn and Olucak, Jan},
	title = {{CaΣoS}: {A} nonlinear sum-of-squares optimization suite},
	booktitle = {2025 American Control Conference},
	address = {Denver, CO},
	year = {2025},
	pages = {1659--1666},
	doi = {10.23919/ACC63710.2025.11107794},
}

@misc{Olucak2026,
      title={On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems}, 
      author={Olucak, Jan and Cunis, Torbjørn},
      year={2026},
      eprint={2602.02394},
      archivePrefix={arXiv},
      url={https://arxiv.org/abs/2602.02394}, 
}

Applications

We provide the source code for our benchmarks and comparisons:

1. Implementation details and source code for CaΣoS: A nonlinear sum-of-squares optimization suite, DaRUS, 2024. doi: 10.18419/DARUS-4499
2. Supplementary Material for Sequential Quadratic Sum-of-squares Programming for Nonlinear Control Systems, DaRUS, 2026. doi: 10.18419/DARUS-5677

Further applications of CaΣoS include:

• F. Geyer, F. Tuttas, W. Fichter, and T. Cunis, ‘Sum-of-Squares Stability Verification on Manifolds with Applications in Spacecraft Attitude Control’, European Journal of Control, 2026, In press. doi: 10.1016/j.ejcon.2026.101587, Source code

• R. Loureiro and T. Cunis, ‘Nonlinear Observer Synthesis for Stochastic Polynomial Dynamical Systems’, in 2025 American Control Conference, (Denver, CO), 2025, pp. 2509–2514. doi: 10.23919/ACC63710.2025.11107965

• R. Loureiro and T. Cunis, ‘Estimating Robust Regions of Attraction with Uncertain Equilibrium Points’, in 2025 American Control Conference, (Denver, CO), 2025, pp. 1045–1050. doi: 10.23919/ACC63710.2025.11107427

• J. Olucak, A. C. B. de Oliveira, and T. Cunis, ‘Safe-by-Design: Approximate Nonlinear Model Predictive Control with Realtime Feasibility’, Preprint. arXiv: 2509.22422, Source code

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