The Schur Complement Revisited

The classical Schur complement provides a compact and enlightening way to d describe various matrix factorizations. In modern large-scale linear and quadratic programming, the Schur complement allows a sequence of related systems of equations to be solved using a fixed sparse factorization and a (usually dense) factorization whose size increases with the number of iterations. We describe the application and pedagogical usefulness of the Schur complement in sparse convex and indefinite quadratic programs.