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Differential-Algebraic Approach to Linear Programming

Author

Listed:
  • M. Xiong

    (University of Texas at Houston)

  • J. Wang

    (Chinese University of Hong Kong)

  • P. Wang

    (James Madison University)

Abstract

This paper presents a differential-algebraic approach for solving linear programming problems. The paper shows that the differential-algebraic approach is guaranteed to generate optimal solutions to linear programming problems with a superexponential convergence rate. The paper also shows that the path-following interior-point methods for solving linear programming problems can be viewed as a special case of the differential-algebraic approach. The results in this paper demonstrate that the proposed approach provides a promising alternative for solving linear programming problems.

Suggested Citation

  • M. Xiong & J. Wang & P. Wang, 2002. "Differential-Algebraic Approach to Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 443-470, August.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:2:d:10.1023_a:1016095904048
    DOI: 10.1023/A:1016095904048
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    References listed on IDEAS

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    1. Irvin J. Lustig & Roy E. Marsten & David F. Shanno, 1994. "Rejoinder—The Last Word on Interior Point Methods for Linear Programming—For Now," INFORMS Journal on Computing, INFORMS, vol. 6(1), pages 35-36, February.
    2. 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.
    3. Robert E. Bixby & John W. Gregory & Irvin J. Lustig & Roy E. Marsten & David F. Shanno, 1992. "Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods," Operations Research, INFORMS, vol. 40(5), pages 885-897, October.
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