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A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation

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  • E. Nagy, Marianna
  • Varga, Anita

Abstract

In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step-size, interior point algorithms can be divided into two main groups, short-step and long-step methods. In practice, long-step variants perform better, but usually, a better theoretical complexity can be achieved for the short-step methods. One of the exceptions is the large-update algorithm of Ai and Zhang. The new wide neighbourhood and the main characteristics of the presented algorithm are based on their approach. In addition, we use the algebraic equivalent transformation technique by Darvay to determine the search directions of the method.

Suggested Citation

  • E. Nagy, Marianna & Varga, Anita, 2021. "A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation," Corvinus Economics Working Papers (CEWP) 2021/06, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2021/06
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    File URL: https://unipub.lib.uni-corvinus.hu/6771/
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    References listed on IDEAS

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    1. Y. Q. Bai & G. Lesaja & C. Roos & G. Q. Wang & M. El Ghami, 2008. "A Class of Large-Update and Small-Update Primal-Dual Interior-Point Algorithms for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 341-359, September.
    2. Nikolaos Ploskas & Nikolaos Samaras, 2017. "Correction to: Linear Programming Using MATLAB®," Springer Optimization and Its Applications, in: Linear Programming Using MATLAB®, pages E1-E3, Springer.
    3. Ilan Adler & Narendra Karmarkar & Mauricio G. C. Resende & Geraldo Veiga, 1989. "Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm," INFORMS Journal on Computing, INFORMS, vol. 1(2), pages 84-106, May.
    4. Zsolt Darvay & Petra Renáta Takács, 2018. "Large-step interior-point algorithm for linear optimization based on a new wide neighbourhood," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 551-563, September.
    5. Nikolaos Ploskas & Nikolaos Samaras, 2017. "Linear Programming Using MATLAB®," Springer Optimization and Its Applications, Springer, number 978-3-319-65919-0, December.
    6. Zs. Darvay & T. Illés & B. Kheirfam & P. R. Rigó, 2020. "A corrector–predictor interior-point method with new search direction for linear optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1123-1140, September.
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    Cited by:

    1. Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2023. "60 years of OR in Slovenia: development from a first conference to a vibrant community," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 681-690, September.

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    More about this item

    Keywords

    Mathematical programming; Linear optimization; Interior point algorithms; Algebraic equivalent transformation technique;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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