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Rank-one techniques in log-barrier function methods for linear programming

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Abstract

This short paper presents a primal interior-point method for linear programming. The method can be viewed as a modification of the methods developed in Refs. 1–6. In each iteration, it computes an approximately projected Newton direction and needsO(n 2.5) arithmetic operations to make the log-barrier function significantly decrease. It requires\(O(\sqrt {nL} )\) iterations, so that the total complexity isO(n 3 L).

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Additional information

This research was supported by the Natural Science Foundation of China and the Tian Yuan Foundation for Mathematics. We are also very grateful to the referees for the many constructive comments and corrections useful for revising this paper.

Communicated by A. V. Fiacco

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Wu, S.Q., Wu, F. Rank-one techniques in log-barrier function methods for linear programming. J Optim Theory Appl 82, 405–413 (1994). https://doi.org/10.1007/BF02191863

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Key Words

  • Linear programming
  • interior-point methods
  • Karmarkar's method
  • log-barrier function
  • rank-one techniques
  • computational complexity