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A Centered Projective Algorithm for Linear Programming

Author

Listed:
  • Michael J. Todd

    (Cornell University)

  • Yinyu Ye

    (Stanford University)

Abstract

We describe a projective algorithm for linear programming that shares features with Karmarkar's projective algorithm and its variants and with the path-following methods of Gonzaga, Kojima-Mizuno-Yoshise, Monteiro-Adler, Renegar, Vaidya and Ye. It operates in a primal-dual setting, stays close to the central trajectories, and converges in O(square root of n times L) iterations like the latter methods. (Here n is the number of variables and L the input size of the problem). However, it is motivated by seeking reductions in a suitable potential function as in projective algorithms, and the approximate centering is an automatic byproduct of our choice of potential function.

Suggested Citation

  • Michael J. Todd & Yinyu Ye, 1988. "A Centered Projective Algorithm for Linear Programming," Cowles Foundation Discussion Papers 861, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:861
    Note: CFP 769.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d08/d0861.pdf
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    References listed on IDEAS

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    1. Kurt M. Anstreicher, 1989. "The Worst-Case Step in Karmarkar's Algorithm," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 294-302, May.
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    Cited by:

    1. Freund, Robert Michael., 1989. "A potential-function reduction algorithm for solving a linear program directly from an infeasible "warm start"," Working papers 3079-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Bertsimas, Dimitris. & Luo, Xiaodong., 1993. "On the worst case complexity of potential reduction algorithms for linear programming," Working papers 3558-93., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June.

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    1. Bertsimas, Dimitris. & Luo, Xiaodong., 1993. "On the worst case complexity of potential reduction algorithms for linear programming," Working papers 3558-93., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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