Supplementary Material for On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems

Version 2.0
Olucak, Jan; Cunis, Torbjørn, 2026, "Supplementary Material for On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems", https://doi.org/10.18419/DARUS-5677, DaRUS, V2
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Description
This repository contains supplementary material for the paper "On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems" submitted to Mathematical Programming Computation. It contains the MATLAB source code to reproduce the results from the paper.

Requirements and Setup:
The implementation of the proposed filter line search algorithm is provided in the CaΣoS toolbox. A frozen copy of it is provided as .zip, below.
1. Select all files below, i.e., all .zip folder, the .m scripts, and additional documents and download them. You should obtain one main .zip file. Unzip the main file and files in the underlying folder.
2. Download CasADi v3.6.7 and add it to your Matlab path.
3. Download and install MOSEK v11.1.8 , and add the solver to the Matlab path. An academic license can be obtained here.
4. Add the CaΣoS root folder (the one that contains the directory +casos) to your Matlab path.

If installed correctly, you can execute the corresponding files as outlined below for reproduction.

The files can be also found in the corresponding Github Repository.

In case you encounter any issues or for questions, please contact the corresponding authors.

Implementation Details:
We provide an additional file "Implementation_Details_Sequential_SOS.pdf", which provides more information of the implementation in CaΣoS. For instance, this document provides a class diagram and describes the folder structure.

Onboarding Tutorial
For a simple onboarding process, we provide a tutorial.m file. This file implements a simple example and guides the user through the solver build process. Due to its simplicity, this file is recommended for debugging purposes of the proposes filter line search algorithm.

Running the Benchmarks:
1. Navigate to the corresponding folder.
2. Run the MATLAB script either for the sequential approach or for coordinate descent.

An exception is the N-link robot arm example (00_ROA/RobotArm). Use run_Nlink_benchmark.m to either run the benchmark from scratch or to just inspect the results, provided in the corresponding .mat file. (2026-04-07)
Subject Engineering
Keyword Sum-of-Squares, Nonlinear Optimization, Nonlinear Control, Nonlinear Control Theory
Related Publication Is Supplement To: Jan Olucak, Torbjørn Cunis (2026). "On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems," Preprint.arXiv: 2602.02394
Notes More information can be found in the README.md.
License/Data Use Agreement

GPL 3.0 or later

Table
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1 to 10 of 10 Files
Implementation_Details_Sequential_SOS.pdf
Adobe PDF - 208.2 KB
Published Apr 14, 2026
5 Downloads
MD5: 3c061201f52280188e61a976466fd567
Provides more details on the implementation in Matlab and the CaSoS toolbox.
Preview "Implementation_Details_Sequential_SOS.pdf"
00_ROA.zip
Supplementary/ZIP Archive - 8.6 MB
Published Apr 14, 2026
6 Downloads
MD5: b4a11a56db952b92f9921b8f4064b0b9
Contains the F18/A and robot arm ROA benchmark.
Preview "Supplementary/00_ROA.zip"
01_Control_design.zip
Supplementary/ZIP Archive - 771.9 KB
Published Apr 14, 2026
6 Downloads
MD5: 11b5168aababeca1f53d9b8c75d6dfdd
Contains the benchmarks for control design.
Preview "Supplementary/01_Control_design.zip"
02_Reachability.zip
Supplementary/ZIP Archive - 1.0 MB
Published Apr 14, 2026
6 Downloads
MD5: 19e2d392cfb69261afbe3ec88e449e41
Contains the benchmarks for reachability analysis.
Preview "Supplementary/02_Reachability.zip"
03_CBF_CLF.zip
Supplementary/ZIP Archive - 193.5 KB
Published Apr 14, 2026
5 Downloads
MD5: 5f61f352f3c4cf86e275a027c590d263
Contains the timing analysis of the proposed sequential SOS algorithm using a compatible CBF/CLF pair synthesis.
Preview "Supplementary/03_CBF_CLF.zip"
casos.zip
Supplementary/ZIP Archive - 231.8 KB
Published Apr 14, 2026
4 Downloads
MD5: d266763db93359b6c64d31806c16e342
Copy of the CaSoS toolbox v1.0.
Preview "Supplementary/casos.zip"
constraintViolationCheck_comparison.m
Supplementary/MATLAB Source Code - 4.8 KB
Published Apr 14, 2026
4 Downloads
MD5: ad5b395a8c7bd004871a1cfa5e292f63
Script to reprocude the different constraint violation check methods from Section 4.2 in the paper
LICENSE
Supplementary/Plain Text - 35.0 KB
Published Apr 14, 2026
3 Downloads
MD5: e62637ea8a114355b985fd86c9ffbd6e
README.md
Supplementary/Markdown Text - 4.2 KB
Published Apr 14, 2026
4 Downloads
MD5: d74b2d05c067f601b0c21b30231e7dc3
Preview "Supplementary/README.md"
tutorial.m
Supplementary/MATLAB Source Code - 5.1 KB
Published Apr 14, 2026
5 Downloads
MD5: 6cd39e72317afe7ececcf3bea16bffcd
Simple onboarding script to get familiar with the CaSoS toolbox and to understand how to setup the nonconvex SOS problems and solve them with the proposed sequential SOS algorithm.
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Curation Status History
StatusDateAssigner
2026-04-14 13:20:49Torbjörn Cunis
Waiting for Feedback from Author2026-04-13 12:46:11Dorothea Iglezakis
In Review by FoKUS2026-04-09 13:37:59Dorothea Iglezakis
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