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A TAYLOR SERIES EXPANSION METHOD FOR SOLVING LINEAR FRACTIONAL PROGRAMMING PROBLEMS.

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Title: A TAYLOR SERIES EXPANSION METHOD FOR SOLVING LINEAR FRACTIONAL PROGRAMMING PROBLEMS.
Authors: Kumari, Poonam1 poonamkumari1865@gmail.com
Source: Reliability: Theory & Applications. Dec2025, Vol. 20 Issue 4, p513-527. 15p.
Subjects: Fractional programming, Linear programming, Mathematical programming, Taylor's series, Mathematical optimization, Iterative methods (Mathematics), Mathematical bounds, Empirical research
Abstract: This paper proposes an iterative method to solve Linear Fractional Programming (LFP) problems with inequality constraints. The core idea is to approximate the fractional objective function through a series of linear programming (LP) problems, solved successively using updated feasible points. The algorithm begins by selecting a non-zero feasible point that satisfies all inequality constraints. At this point, the fractional objective function is expanded using a first-order Taylor series, resulting in a linear approximation. This converts the LFP problem into a standard LP problem, which can be solved using common optimization techniques such as the simplex method or the graphical method, depending on the problem's size and complexity. The optimal solution of the LP problem is then used as the new feasible point for the next iteration. In each iteration, the fractional objective function is re-linearized around the current solution, and a new LP problem is formed and solved. This process continues until convergence is achieved, that is, when two successive iterations produce the same or sufficiently similar solutions. The final solution is taken as the optimal solution to the original LFP problem. The effectiveness and practical utility of the proposed method are demonstrated through numerical examples. Results indicate that the approach is computationally efficient and provides accurate solutions. Compared to traditional transformation-based techniques, the proposed method avoids the introduction of auxiliary variables or complex reformulations, offering a more intuitive and implementable solution framework. Furthermore, the approach exhibits potential for extension to more complex fractional programming models, including multi-objective and equality-constrained formulations. [ABSTRACT FROM AUTHOR]
Copyright of Reliability: Theory & Applications is the property of International Group on Reliability and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A TAYLOR SERIES EXPANSION METHOD FOR SOLVING LINEAR FRACTIONAL PROGRAMMING PROBLEMS.
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  Data: <searchLink fieldCode="AR" term="%22Kumari%2C+Poonam%22">Kumari, Poonam</searchLink><relatesTo>1</relatesTo><i> poonamkumari1865@gmail.com</i>
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  Data: <searchLink fieldCode="DE" term="%22Fractional+programming%22">Fractional programming</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Taylor's+series%22">Taylor's series</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink><br /><searchLink fieldCode="DE" term="%22Empirical+research%22">Empirical research</searchLink>
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  Data: This paper proposes an iterative method to solve Linear Fractional Programming (LFP) problems with inequality constraints. The core idea is to approximate the fractional objective function through a series of linear programming (LP) problems, solved successively using updated feasible points. The algorithm begins by selecting a non-zero feasible point that satisfies all inequality constraints. At this point, the fractional objective function is expanded using a first-order Taylor series, resulting in a linear approximation. This converts the LFP problem into a standard LP problem, which can be solved using common optimization techniques such as the simplex method or the graphical method, depending on the problem's size and complexity. The optimal solution of the LP problem is then used as the new feasible point for the next iteration. In each iteration, the fractional objective function is re-linearized around the current solution, and a new LP problem is formed and solved. This process continues until convergence is achieved, that is, when two successive iterations produce the same or sufficiently similar solutions. The final solution is taken as the optimal solution to the original LFP problem. The effectiveness and practical utility of the proposed method are demonstrated through numerical examples. Results indicate that the approach is computationally efficient and provides accurate solutions. Compared to traditional transformation-based techniques, the proposed method avoids the introduction of auxiliary variables or complex reformulations, offering a more intuitive and implementable solution framework. Furthermore, the approach exhibits potential for extension to more complex fractional programming models, including multi-objective and equality-constrained formulations. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Reliability: Theory & Applications is the property of International Group on Reliability and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.24412/1932-2321-2025-489-513-527
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      – Code: eng
        Text: English
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      – SubjectFull: Fractional programming
        Type: general
      – SubjectFull: Linear programming
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      – SubjectFull: Mathematical programming
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      – SubjectFull: Taylor's series
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      – SubjectFull: Mathematical optimization
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      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Mathematical bounds
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      – SubjectFull: Empirical research
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      – TitleFull: A TAYLOR SERIES EXPANSION METHOD FOR SOLVING LINEAR FRACTIONAL PROGRAMMING PROBLEMS.
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              M: 12
              Text: Dec2025
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              Y: 2025
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