Improving an interior-point approach for large block-angular problems by hybrid preconditioners
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The computational time required by interior-point methods is often domi- nated by the solution of linear systems of equations. An efficient spec ialized interior-point algorithm for primal block-angular proble ms has been used to solve these systems by combining Cholesky factorizations for the block con- straints and a conjugate gradient based on a power series precon ditioner for the linking constraints. In some problems this power series prec onditioner re- sulted to be inefficient on the last interior-point iterations, wh en the systems became ill-conditioned. In this work this approach is combi ned with a split- ting preconditioner based on LU factorization, which is main ly appropriate for the last interior-point iterations. Computational result s are provided for three classes of problems: multicommodity flows (oriented and no noriented), minimum-distance controlled tabular adjustment for statistic al data protec- tion, and the minimum congestion problem. The results show that , in most cases, the hybrid preconditioner improves the performance an d robustness of the interior-point solver. In particular, for some block-ang ular problems the solution time is reduced by a factor of 10.
CitacióBocanegra, S.; Castro, J.; Oliveira, A.R.L. "Improving an interior-point approach for large block-angular problems by hybrid preconditioners". DR 2012/06 ed. 2012.
Forma partTechnical Report DR 2012/06 UPC-EIO
Versió de l'editorhttp://www-eio.upc.es/~jcastro/publications/reports/dr2012-06.pdf