Solving linear programming problem using approximate optimization method
Keywords:
Linear programming, Duality in linear programming, Approximations with Taylor Series , Python languageAbstract
In this paper, we will define optimization, linear programming, and the duality of linear programming and demonstrate them in practice through several examples in which the Python language was used to display the final outputs using codes for various libraries. We will also illustrate the method of approximation to Tyler by defining the strategy and demonstrating it in practice through an example.
Downloads
References
Luenberger, D. G., & Ye, Y. (1984). Linear and nonlinear programming (Vol. 2). Reading, MA: Addison-Wesley.
Hlawitschka, W. (1994). The empirical nature of Taylor-series approximations to expected utility. The American Economic Review, 84(3), 713-719.
Sanner, M. F. (1999). Python: a programming language for software integration and development. J Mol Graph Model, 17(1), 57-61.
Herrera, F., & Herrera-Viedma, E. (2000). Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets and systems, 115(1), 67-82. DOI: https://doi.org/10.1016/S0165-0114(99)00024-X
Ben-Tal, A., & Nemirovski, A. (2001). Lectures on modern convex optimization: analysis, algorithms, and engineering applications. Society for industrial and applied mathematics. DOI: https://doi.org/10.1137/1.9780898718829
Sun, W., & Yuan, Y. X. (2006). Optimization theory and methods: nonlinear programming (Vol. 1). Springer Science & Business Media.
Arora, R. K. (2015). Optimization: algorithms and applications. CRC Press DOI: https://doi.org/10.1201/b18469
Bertsekas, D. (2015). Convex optimization algorithms. Athena Scientific.
Rao, S. S. (2019). Engineering optimization: theory and practice. John Wiley & Sons.
Rao, S. S. (2019). Engineering optimization: theory and practice. John Wiley & Sons DOI: https://doi.org/10.1002/9781119454816
Andréasson, N., Evgrafov, A., & Patriksson, M. (2020). An introduction to continuous optimization: Foundations and fundamental algorithms. Courier Dover Publications
Osaba, E., Villar-Rodriguez, E., Del Ser, J., Nebro, A. J., Molina, D., LaTorre, A., ... & Herrera, F. (2021)
Alridha, A., Wahbi, F. A., & Kadhim, M. K. (2021). Training analysis of optimization models in machine learning. International Journal of Nonlinear Analysis and Applications, 12(2), 1453-1461.
Alridha, A., Salman, A. M., & Al-Jilawi, A. S. (2021, March). The Applications of NP-hardness optimizations problem. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012179). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1818/1/012179
Salman, A. M., Alridha, A., & Hussain, A. H. (2021, March). Some Topics on Convex Optimization. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012171). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1818/1/012171
Alridha, A., & Al-Jilawi, A. S. (2021, March). Mathematical Programming Computational for Solving NP-Hardness Problem. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012137). IOP Publishing DOI: https://doi.org/10.1088/1742-6596/1818/1/012137
Al-Jilawi, A. S., & Abd Alsharify, F. H. (2022). Review of Mathematical Modelling Techniques with Applications in Biosciences. Iraqi Journal For Computer Science and Mathematics, 3(1), 135-144.
Kadhim, M. K., Wahbi, F. A., & Hasan Alridha, A. (2022). Mathematical optimization modeling for estimating the incidence of clinical diseases. International Journal of Nonlinear Analysis and Applications, 13(1), 185-195.
Alridha, A. H., & Al-Jilawi, A. S. (2022). Solving NP-hard problems using a new relaxation of approximate methods. International Journal of Health Sciences, 6(S3), 523–536. https://doi.org/10.53730/ijhs.v6nS3.5375 DOI: https://doi.org/10.53730/ijhs.v6nS3.5375
Published
How to Cite
Issue
Section
Copyright (c) 2022 International journal of health sciences

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Articles published in the International Journal of Health Sciences (IJHS) are available under Creative Commons Attribution Non-Commercial No Derivatives Licence (CC BY-NC-ND 4.0). Authors retain copyright in their work and grant IJHS right of first publication under CC BY-NC-ND 4.0. Users have the right to read, download, copy, distribute, print, search, or link to the full texts of articles in this journal, and to use them for any other lawful purpose.
Articles published in IJHS can be copied, communicated and shared in their published form for non-commercial purposes provided full attribution is given to the author and the journal. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
This copyright notice applies to articles published in IJHS volumes 4 onwards. Please read about the copyright notices for previous volumes under Journal History.








