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Interior-Point Methods with Decomposition for Solving Large-Scale Linear Programs

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  • G. Y. Zhao

    (National University of Singapore)

Abstract

This paper deals with an algorithm incorporating the interior-point method into the Dantzig–Wolfe decomposition technique for solving large-scale linear programming problems. The algorithm decomposes a linear program into a main problem and a subproblem. The subproblem is solved approximately. Hence, inexact Newton directions are used in solving the main problem. We show that the algorithm is globally linearly convergent and has polynomial-time complexity.

Suggested Citation

  • G. Y. Zhao, 1999. "Interior-Point Methods with Decomposition for Solving Large-Scale Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 169-192, July.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:1:d:10.1023_a:1021850714072
    DOI: 10.1023/A:1021850714072
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    2. John R. Birge & Liqun Qi, 1988. "Computing Block-Angular Karmarkar Projections with Applications to Stochastic Programming," Management Science, INFORMS, vol. 34(12), pages 1472-1479, December.
    3. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
    4. Roy Marsten & Radhika Subramanian & Matthew Saltzman & Irvin Lustig & David Shanno, 1990. "Interior Point Methods for Linear Programming: Just Call Newton, Lagrange, and Fiacco and McCormick!," Interfaces, INFORMS, vol. 20(4), pages 105-116, August.
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    Cited by:

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