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On two homogeneous self-dual approaches to linear programming and its extensions

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Abstract.

We investigate the relation between interior-point algorithms applied to two homogeneous self-dual approaches to linear programming, one of which was proposed by Ye, Todd, and Mizuno and the other by Nesterov, Todd, and Ye. We obtain only a partial equivalence of path-following methods (the centering parameter for the first approach needs to be equal to zero or larger than one half), whereas complete equivalence of potential-reduction methods can be shown. The results extend to self-scaled conic programming and to semidefinite programming using the usual search directions.

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Author information

Authors and Affiliations

  1. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan, e-mail: mizuno@ism.ac.jp, , , , , , JP

    Shinji Mizuno

  2. School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, USA, e-mail: miketodd@cs.cornell.edu, , , , , , US

    Michael J. Todd

Authors
  1. Shinji Mizuno
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  2. Michael J. Todd
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Received: July 1998 / Accepted: September 2000¶Published online November 17, 2000

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Mizuno, S., Todd, M. On two homogeneous self-dual approaches to linear programming and its extensions. Math. Program. 89, 517–534 (2001). https://doi.org/10.1007/PL00011413

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  • DOI: https://doi.org/10.1007/PL00011413