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Large step volumetric potential reduction algorithms for linear programming

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Abstract

We consider the construction of potential reduction algorithms using volumetric, and mixed volumetric — logarithmic, barriers. These are true “large step” methods, where dual updates produce constant-factor reductions in the primal-dual gap. Using a mixed volumetric — logarithmic barrier we obtain an\(O(\sqrt {nmL} )\) iteration algorithm, improving on the best previously known complexity for a large step method. Our results complement those of Vaidya and Atkinson on small step volumetric, and mixed volumetric — logarithmic, barrier function algorithms. We also obtain simplified proofs of fundamental properties of the volumetric barrier, originally due to Vaidya.

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Authors and Affiliations

  1. Department of Management Sciences, University of Iowa, 52242, Iowa City, IA, USA

    Kurt M. Anstreicher

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  1. Kurt M. Anstreicher
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Research supported by a Summer Research Grant from the College of Business Administration, University of Iowa.

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Anstreicher, K.M. Large step volumetric potential reduction algorithms for linear programming. Ann Oper Res 62, 521–538 (1996). https://doi.org/10.1007/BF02206828

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