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A reduced-gradient variant of Karmarkar's algorithm and null-space projections

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Abstract

This paper discusses the relationship between Karmarkar's new method for linear programming and the traditional simplex method. It is shown how null-space Karmarkar projections can be done using a basis matrix to compute the projections in the null space. Preliminary computational evidence shows that problems exist in the choice of a basis matrix, but that, given a basis, very inexact and computationally efficient projections are computationally sound.

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References

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Author notes

  1. D. F. Shanno (Professor)

    Present address: Busch Campus, Rutgers Center for Operations Research, Hill Center for Mathematical Sciences, 08903, New Brunswick, New Jersey

Authors and Affiliations

  1. Graduate School of Administration, University of California, Davis, California

    D. F. Shanno (Professor)

  2. Department of Management Information Systems, College of Business and Public Administration, University of Arizona, Tucson, Arizona

    R. E. Marsten (Professor)

Authors
  1. D. F. Shanno
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  2. R. E. Marsten
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Shanno, D.F., Marsten, R.E. A reduced-gradient variant of Karmarkar's algorithm and null-space projections. J Optim Theory Appl 57, 383–397 (1988). https://doi.org/10.1007/BF02346159

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