A simple preprocessing algorithm for semidefinite programming

Abstract

We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It often detects infeasibility. Our algorithm does not rely on any optimization solver: the only subroutine it needs is Cholesky factorization, hence it can be implemented with a few lines of code in machine precision. We present computational results on a set of problems arising mostly from polynomial optimization.