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A corrector–predictor interior-point method with new search direction for linear optimization

Author

Listed:
  • Zs. Darvay

    (Babeş-Bolyai University)

  • T. Illés

    (Budapest University of Technology and Economics)

  • B. Kheirfam

    (Azarbaijan Shahid Madani University)

  • P. R. Rigó

    (Babeş-Bolyai University
    Budapest University of Technology and Economics)

Abstract

We introduce a feasible corrector–predictor interior-point algorithm (CP IPA) for solving linear optimization problems which is based on a new search direction. The search directions are obtained by using the algebraic equivalent transformation (AET) of the Newton system which defines the central path. The AET of the Newton system is based on the map that is a difference of the identity function and square root function. We prove global convergence of the method and derive the iteration bound that matches best iteration bounds known for these types of methods. Furthermore, we prove the practical efficiency of the new algorithm by presenting numerical results. This is the first CP IPA which is based on the above mentioned search direction.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:28:y:2020:i:3:d:10.1007_s10100-019-00622-3
    DOI: 10.1007/s10100-019-00622-3
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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. Terlaky, Tamas, 2001. "An easy way to teach interior-point methods," European Journal of Operational Research, Elsevier, vol. 130(1), pages 1-19, April.
    3. Guo-qiang Wang & Yu-jing Yue & Xin-zhong Cai, 2009. "Weighted-path-following interior-point algorithm to monotone mixed linear complementarity problem," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 435-445, December.
    4. G. Q. Wang, 2012. "A New Polynomial Interior-Point Algorithm For The Monotone Linear Complementarity Problem Over Symmetric Cones With Full Nt-Steps," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-20.
    5. Potra, Florian A., 2002. "The Mizuno-Todd-Ye algorithm in a larger neighborhood of the central path," European Journal of Operational Research, Elsevier, vol. 143(2), pages 257-267, December.
    6. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
    7. Behrouz Kheirfam, 2015. "A Corrector–Predictor Path-Following Method for Convex Quadratic Symmetric Cone Optimization," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 246-260, January.
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    Cited by:

    1. Marianna E.-Nagy & Anita Varga, 2023. "A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation," 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 691-711, September.
    2. Darvay, Zsolt & Illés, Tibor & Rigó, Petra Renáta, 2022. "Predictor-corrector interior-point algorithm for P*(κ)-linear complementarity problems based on a new type of algebraic equivalent transformation technique," European Journal of Operational Research, Elsevier, vol. 298(1), pages 25-35.
    3. Marianna E.-Nagy & Anita Varga, 2023. "A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation," 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 691-711, September.
    4. Botond Bertók & Tibor Csendes & Gábor Galambos, 2021. "Operations research in Hungary: VOCAL 2018," 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. 29(2), pages 379-386, June.

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