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Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming

Author

Listed:
  • Fabio Vitor

    (University of Nebraska at Omaha)

  • Todd Easton

    (The University of Utah)

Abstract

The vast majority of linear programming interior point algorithms successively move from an interior solution to an improved interior solution by following a single search direction, which corresponds to solving a one-dimensional subspace linear program at each iteration. On the other hand, two-dimensional search interior point algorithms select two search directions, and determine a new and improved interior solution by solving a two-dimensional subspace linear program at each step. This paper presents primal and dual two-dimensional search interior point algorithms derived from affine and logarithmic barrier search directions. Both search directions are determined by randomly partitioning the objective function into two orthogonal vectors. Computational experiments performed on benchmark instances demonstrate that these new methods improve the average CPU time by approximately 12% and the average number of iterations by 14%.

Suggested Citation

  • Fabio Vitor & Todd Easton, 2022. "Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming," Computational Optimization and Applications, Springer, vol. 83(1), pages 211-246, September.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00385-9
    DOI: 10.1007/s10589-022-00385-9
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    References listed on IDEAS

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    1. Mousaab Bouafia & Djamel Benterki & Adnan Yassine, 2016. "An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 528-545, August.
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    6. Fabio Vitor & Todd Easton, 2018. "The double pivot simplex method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 109-137, February.
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