1 research outputs found
Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone
We develop a practical semidefinite programming (SDP) facial reduction
procedure that utilizes computationally efficient approximations of the
positive semidefinite cone. The proposed method simplifies SDPs with no
strictly feasible solution (a frequent output of parsers) by solving a sequence
of easier optimization problems and could be a useful pre-processing technique
for SDP solvers. We demonstrate effectiveness of the method on SDPs arising in
practice, and describe our publicly-available software implementation. We also
show how to find maximum rank matrices in our PSD cone approximations (which
helps us find maximal simplifications), and we give a post-processing procedure
for dual solution recovery that generally applies to facial-reduction-based
pre-processing techniques. Finally, we show how approximations can be chosen to
preserve problem sparsity.Comment: Expanded computational results, added results on sparsity, and
revised dual solution recovery sectio