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Volume 17
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10.3390/a17070303
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Article

On Implementing a Two-Step Interior Point Method for Solving Linear Programs

by
Sajad Fathi Hafshejani
*,
Daya Gaur
* and
Robert Benkoczi
Department of Math and Computer Science, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada
*
Authors to whom correspondence should be addressed.
Algorithms 2024, 17(7), 303; https://doi.org/10.3390/a17070303
Submission received: 3 June 2024 / Revised: 2 July 2024 / Accepted: 5 July 2024 / Published: 8 July 2024
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 2nd Edition)
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Abstract

A new two-step interior point method for solving linear programs is presented. The technique uses a convex combination of the auxiliary and central points to compute the search direction. To update the central point, we find the best value for step size such that the feasibility condition is held. Since we use the information from the previous iteration to find the search direction, the inverse of the system is evaluated only once every iteration. A detailed empirical evaluation is performed on NETLIB instances, which compares two variants of the approach to the primal-dual log barrier interior point method. Results show that the proposed method is faster. The method reduces the number of iterations and CPU time(s) by 27% and 18%, respectively, on NETLIB instances tested compared to the classical interior point algorithm.
Keywords: linear programming; interior point method; Newton method linear programming; interior point method; Newton method

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MDPI and ACS Style

Fathi Hafshejani, S.; Gaur, D.; Benkoczi, R. On Implementing a Two-Step Interior Point Method for Solving Linear Programs. Algorithms 2024, 17, 303. https://doi.org/10.3390/a17070303

AMA Style

Fathi Hafshejani S, Gaur D, Benkoczi R. On Implementing a Two-Step Interior Point Method for Solving Linear Programs. Algorithms. 2024; 17(7):303. https://doi.org/10.3390/a17070303

Chicago/Turabian Style

Fathi Hafshejani, Sajad, Daya Gaur, and Robert Benkoczi. 2024. "On Implementing a Two-Step Interior Point Method for Solving Linear Programs" Algorithms 17, no. 7: 303. https://doi.org/10.3390/a17070303

APA Style

Fathi Hafshejani, S., Gaur, D., & Benkoczi, R. (2024). On Implementing a Two-Step Interior Point Method for Solving Linear Programs. Algorithms, 17(7), 303. https://doi.org/10.3390/a17070303

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