Sum-of-squares chordal decomposition of polynomial matrix inequalities: Examples

This repository contains MATLAB scripts that implement the numerical examples in the following paper:

1. Zheng, Y. and Fantuzzi, G. (2020). Sum-of-squares chordal decomposition of polynomial matrix inequalities, arXiv:2007.11410 [math.OC].

Instructions

To run the scripts in this repository you need a working MATLAB installation. In addition, please install:

• The optimization toolbox YALMIP
• An SDP solver compatible with YALMIP. We recommend MOSEK, but any of the solvers listed here should work.

We adapted the sos.csp option in YALMIP to exploit chordal sparsity described in our paper. For this option, please

• Copy corrsparsity.m and cliquesFromSpMatD.m to the folder of /modules/sos, and replace the original corrsparsity.m (cliquesFromSpMatD.m is copied from the SparseCoLO package)

Additional references

1. Zheng, Y., Fantuzzi, G. and Papachristodoulou, A. (2019). Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials. In: Proceedings of the 2019 American Control Conference, pp. 5513-5518. [Publisher Link] [Open Access Link]

2. Zheng, Y., Fantuzzi, G. and Papachristodoulou, A. (2018). Decomposition and completion of sum-of-squares matrices. In: Proceedings of the 57th IEEE Conference on Decision and Control, pp. 4026-4031. [Publisher Link] [Open Access Link]

3. Waki, H., Kim, S., Kojima, M. and Muramatsu, M. (2006). Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity. SIAM Journal on Optimization, 17(1), 218-242. [Publisher Link]

Troubleshooting

If you have any trouble running the scripts in this repository, please email Yang Zheng.