  Interior point methods are widely used for different types of mathematical
optimization problems. Many implementations of interior point methods in use
today rely on direct linear solvers to solve systems of equations in each
iteration. The need to solve ever larger optimization problems more efficiently
and the rise of hardware accelerators for general purpose computing has led to
a large interest in using iterative linear solvers instead, with the major
issue being inevitable ill-conditioning of the linear systems arising as the
optimization progresses. We investigate the use of Krylov solvers for interior
point methods in solving optimization problems from radiation therapy and
support vector machines. We implement a prototype interior point method using a
so called doubly augmented formulation of the Karush-Kuhn-Tucker linear system
of equations, originally proposed by Forsgren and Gill, and evaluate its
performance on real optimization problems from radiation therapy and support
vector machines. Crucially, our implementation uses a preconditioned conjugate
gradient method with Jacobi preconditioning internally. Our measurements of the
conditioning of the linear systems indicate that the Jacobi preconditioner
improves the conditioning of the systems to a degree that they can be solved
iteratively, but there is room for further improvement in that regard.
Furthermore, profiling of our prototype code shows that it is suitable for GPU
acceleration, which may further improve its performance in practice. Overall,
our results indicate that our method can find solutions of acceptable accuracy
in reasonable time, even with a simple Jacobi preconditioner.
