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Improving an interior-point approach for large block-angular problems by hybrid preconditioners

Silvana Bocanegra (silvana***at***deinfo.ufrpe.br)
Jordi Castro (jordi.castro***at***upc.edu)
Aurelio R.L. Oliveira (aurelio***at***ime.unicamp.br)

Abstract: The computational time required by interior-point methods is often dominated by the solution of linear systems of equations. An efficient specialized interior-point algorithm for primal block-angular problems has been used to solve these systems by combining Cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints. In some problems this power series preconditioner resulted to be inefficient on the last interior-point iterations, when the systems became ill-conditioned. In this work this approach is combined with a splitting preconditioner based on LU factorization, which is mainly appropriate for the last interior-point iterations. Computational results are provided for three classes of problems: multicommodity flows (oriented and nonoriented), minimum-distance controlled tabular adjustment for statistical data protection, and the minimum congestion problem. The results show that, in most cases, the hybrid preconditioner improves the performance and robustness of the interior-point solver. In particular, for some block-angular problems the solution time is reduced by a factor of $10$.

Keywords: Interior-point methods ; Large-scale optimization ; Preconditioned conjugate gradient ; Structured problems

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Research Report UPC-DEIO DR 2012-06. Dept. of Statistics and Operations Research, Universitat Polit├Ęcnica de Catalunya, 2012.

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Entry Submitted: 09/20/2012
Entry Accepted: 09/20/2012
Entry Last Modified: 09/20/2012

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