Interior point methods (IPMs) have shown to behave very well in some classes of large-scale structured problems. We will discuss a successful approach for block-angular problems that relies on the sensible combination of Cholesky factorizations and preconditioned conjugate gradient for the normal equations. However, the iterative solver becomes inefficient in the last interior point iterations, when the systems became ill-conditioned. In the first part of the talk we will discuss two successful approaches for improving the iterative solver. The first one is based on a regularization of the problem. The second one considers a hybrid preconditioner that differentiates between the first and last interior point iterations. In the second part of the talk we will present a real-world application from the field of "statistical disclosure control". The goal is to protect statistical tables before they are released. This is a main concern for national statistical institutes. It results in a large optimization problem. We will show that for some tables the resulting problems exhibit a block-angular structure, which is efficiently solved by the specialized IPM.
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