### Jordi Castro (Universitat Politècnica de Catalunya, Barcelona)

#### Improving iterative solvers in IPMs: regularizations and hybrid preconditioners

*Wednesday 10 October 2012 at 15.30, JCMB 5215*

##### Abstract

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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