  Interior-point methods for linear programming problems require the repeated
solution of a linear system of equations. Solving these linear systems is
non-trivial due to the severe ill-conditioning of the matrices towards
convergence. This issue can be alleviated by incorporating suitable
regularization terms in the linear programming problem. Regularization also
allows us to efficiently handle rank deficient constraint matrices. We provide
a convergence analysis of a regularized inexact interior-point method. The term
`inexact' refers to the fact that we do not need to compute the true solution
of the linear system of equations, only an approximation thereof. The
formulation of the algorithm is sufficiently general such that specialized
linear algebra routines developed in other work on inexact interior-point
methods can also be incorporated in our regularized framework. In this work, we
exploit the inexactness by using a mixed-precision solver for the linear system
of equations. More specifically, we perform a Cholesky factorization in IEEE
single precision and use it as a preconditioner for the Conjugate Gradient
method. Numerical experiments illustrate the benefits of this approach applied
to linear programming problems with a dense constraint matrix.
