Weakly infeasible SDPs from Pataki-Touzov

This page contains problem instances generated in the paper

• An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone

by G. Pataki and A. Touzov

The “clean” instances are accompanied by a visualization, in the “img” directory. Some of the matrices prove infeasibility of the SDP, and some prove not-strong-infeasibility.

• For example, here is a visualization for the SDP coming from trying to find a sum-of-squares decomposition of the Motzkin polynomial. This SDP is described in detail in the paper.

• Download mini instances from here (approx. 0.8 MB)
• Download small instances from here (approx. 4 MB)
• Download medium instances from here (approx. 28 MB)
• Download large instances from here (approx. 196 MB)
• Download all instances from here (approx. 228 MB)

Feel free to send me comments, suggestions, or email me if you find any broken links.