Preprocessing sparse semidefinite programs via matrix completion

Considering that preprocessing is an important phase in linear programing, it should be more systematically incorporated in semidefinite programing ( SDP) solvers. The conversion method proposed by the authors [Fukuda, M., Kojima, M., Murota, K. and Nakata, K., 2000, SIAM Journal on Optimization, 11, 647 - 674 and Nakata, K., Fujisawa, K., Fukuda, M., Kojima, M. and Murota, K., 2003, Mathematical Programming ( Series B), 95, 303 - 327] is a preprocessing method for sparse SDPs based on matrix completion. This article proposed a new version of the conversion method, which employs a flop estimation function inside its heuristic procedure. Extensive numerical experiments are included showing the advantage of preprocessing by the conversion method for certain classes of very sparse SDPs.