SDPs with positive duality gaps

This page was last updated on jan 4, 2019.

This page contains problem instances generated in the paper

• On positive duality gaps in semidefinite programming , G. Pataki

The interesting feature of these SDPs is that the positive gap can be verified in exact arithmetic by hand. However, these SDPs cannot be solved by SDP solvers.

The instances (in Sedumi format, in zip files) are here:

• Single sequence, finite gap, clean SDPs
• Single sequence, finite gap, messy SDPs
• Single sequence, infinite gap, clean SDPs
• Single sequence, infinite gap, messy SDPs

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