Mathematical Programming

, Volume 59, Issue 1, pp 133–150

Combining phase I and phase II in a potential reduction algorithm for linear programming

  • Michael J. Todd

DOI: 10.1007/BF01581241

Cite this article as:
Todd, M.J. Mathematical Programming (1993) 59: 133. doi:10.1007/BF01581241


This paper describes an affine potential reduction algorithm for linear programming that simultaneously seeks feasibility and optimality. The algorithm is closely related to a similar method of Anstreicher. The new features are that we use a two-dimensional programming problem to derive better lower bounds than Anstreicher, that our direction-finding subproblem treats phase I and phase II more symmetrically, and that we do not need an initial lower bound. Our method also allows for the generation of a feasible solution (so that phase I is terminated) during the course of the iterations, and we describe two ways to encourage this behavior.

Key words

Linear programming interior-point methods combined phase I—phase II 

Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • Michael J. Todd
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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