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Sparsity preserving preconditioners for linear systems in interior-point methods

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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.

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Acknowledgments

This work was partially funded by Projects Number 174010 and 174033, Ministry of Science, Technology and Development, Republic of Serbia. The authors would like to thank the two anonymous referees for their comments and observations which have helped to improve the presentation of this paper.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Milan D. Dražić

  2. Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000, Belgrade, Serbia

    Rade P. Lazović & Vera V. Kovačević-Vujčić

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  1. Milan D. Dražić
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  2. Rade P. Lazović
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  3. Vera V. Kovačević-Vujčić
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Correspondence to Milan D. Dražić.

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Dražić, M.D., Lazović, R.P. & Kovačević-Vujčić, V.V. Sparsity preserving preconditioners for linear systems in interior-point methods. Comput Optim Appl 61, 557–570 (2015). https://doi.org/10.1007/s10589-015-9735-7

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