Annals of Operations Research

, Volume 62, Issue 1, pp 521–538 | Cite as

Large step volumetric potential reduction algorithms for linear programming

  • Kurt M. Anstreicher
Article

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.

Keywords

Linear programming interior algorithm potential reduction volumetric barrier 
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Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Kurt M. Anstreicher
    • 1
  1. 1.Department of Management SciencesUniversity of IowaIowa CityUSA

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