Sparsity preserving preconditioners for linear systems in interior-point methods

Milan Dražić (), Rade Lazović () and Vera Kovačević-Vujčić ()

Computational Optimization and Applications, 2015, vol. 61, issue 3, 557-570

Abstract: Systems of normal equations arising in interior-point methods for linear programming in the case of a degenerate optimal face have highly ill-conditioned coefficient matrices. In 2004, Monteiro et al. (SIAM J Optim 15:96–100, 2004 ) proposed a preconditioner which guarantees uniform well-conditionedness. However, the proposed preconditioner may lead to considerable loss of sparsity. Our approach is directed towards a generalization of the proposed preconditioner which makes a balance between sparsity and well-conditionedness. Experimental results on Netlib instances show the effects of the new approach. Copyright Springer Science+Business Media New York 2015

Keywords: Linear programming; Interior-point methods; Condition number; Preconditioning (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-015-9735-7

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