A Two-Step Pre-Processing for Semidefinite Programming

Vyacheslav Kungurtsev, Jakub Marecek

Abstract: In semidefinite programming (SDP), a number of pre-processing techniques have been developed, including procedures based on chordal decomposition, which exploit sparsity in the semidefinite program in order to reduce the dimension of individual constraints, and procedures based on facial reduction, which reduces the dimension of the problem by removing redundant rows and columns. So far, these have been studied in isolation. We show that these techniques are, in fact, complementary. In computational experiments, we show that a two-step pre-processing followed by a standard interior-point method outperforms the interior point method, with or without either of the pre-processing techniques, by a considerable margin.