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Differential-Algebraic Approach to Linear Programming

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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.

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Authors and Affiliations

  1. School of Public Health, University of Texas at Houston, Houston, Texas

    M. Xiong (Associate Professor)

  2. Department of Automation and Computer-Aided Engineering, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    J. Wang (Professor)

  3. Department of Information and Decision Sciences, James Madison University, Harrisonburg, Virginia

    P. Wang (Associate Professor)

Authors
  1. M. Xiong
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  2. J. Wang
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  3. P. Wang
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Xiong, M., Wang, J. & Wang, P. Differential-Algebraic Approach to Linear Programming. Journal of Optimization Theory and Applications 114, 443–470 (2002). https://doi.org/10.1023/A:1016095904048

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