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Interval division and linearization algorithm for minimax linear fractional program

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Abstract

This paper constructs an interval partition linearization algorithm for solving minimax linear fractional programming (MLFP) problem. In this algorithm, MLFP is converted and decomposed into a series of linear programs by dividing the outer 1-dimensional space of the equivalent problem (EP) into polynomially countable intervals. To improve the computational efficiency of the algorithm, two new acceleration techniques are introduced, in which the regions in outer space where the optimal solution of EP does not exist are largely deleted. In addition, the global convergence of the proposed algorithm is summarized, and its computational complexity is illustrated to reveal that it is a fully polynomial time approximation scheme. Finally, the numerical results demonstrate that the proposed algorithm is feasible and effective.

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Data availability

The data in Tables 1, 2, 3, 4, 5, and 6 are obtained by recompiling the pseudo-code in [26, 27] and experimenting in the same operating environment as our algorithm.

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Funding

This research is supported by the National Natural Science Foundation of China under Grant (11961001), the Construction Project of first-class subjects in Ningxia higher Education (NXYLXK2017B09), and the major proprietary funded project of North Minzu University (ZDZX201901).

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Authors and Affiliations

  1. School of Civil and Hydraulic Engineering, Ningxia University, Yinchuan, 750021, China

    Bo Zhang

  2. Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan, 750021, China

    Yuelin Gao & Xia Liu

  3. Ningxia Province Key Laboratory of Intelligent Information and Data Processing, North Minzu University, Yinchuan, 750021, China

    Yuelin Gao & Xia Liu

  4. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China

    Xiaoli Huang

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  1. Bo Zhang
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  2. Yuelin Gao
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Correspondence to Yuelin Gao.

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Zhang, B., Gao, Y., Liu, X. et al. Interval division and linearization algorithm for minimax linear fractional program. Numer Algor 95, 839–858 (2024). https://doi.org/10.1007/s11075-023-01591-0

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  • DOI: https://doi.org/10.1007/s11075-023-01591-0

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