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A primal-dual interior-point method for linear programming based on a weighted barrier function

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Abstract

One motivation for the standard primal-dual direction used in interior-point methods is that it can be obtained by solving a least-squares problem. In this paper, we propose a primal-dual interior-point method derived through a modified least-squares problem. The direction used is equivalent to the Newton direction for a weighted barrier function method with the weights determined by the current primal-dual iterate. We demonstrate that the Newton direction for the usual, unweighted barrier function method can be derived through a weighted modified least-squares problem. The algorithm requires a polynomial number of iterations. It enjoys quadratic convergence if the optimal vertex is nondegenerate.

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Authors and Affiliations

  1. Department of mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York

    Z. Y. Cheng (Graduate Student) & J. E. Mitchell (Associate Professor)

Authors
  1. Z. Y. Cheng
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  2. J. E. Mitchell
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Additional information

Communicated by R. A. Tapia

The research of the second author was supported in part by ONR Grants N00014-90-J-1714 and N00014-94-1-0391.

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Cheng, Z.Y., Mitchell, J.E. A primal-dual interior-point method for linear programming based on a weighted barrier function. J Optim Theory Appl 87, 301–321 (1995). https://doi.org/10.1007/BF02192566

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