数学季刊 ›› 2026, Vol. 41 ›› Issue (1): 50-59.doi: 10.13371/j.cnki.chin.q.j.m.2026.01.004

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极小化线性分式函数的全局优化算法

  

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
  • 收稿日期:2025-04-07 出版日期:2026-03-30 发布日期:2026-03-30
  • 作者简介:ZHAO Peng (2000-), male, native of Xinxiang, Henan, master student of North China University of Water Resources and Electric Power, engages in optimization theory and application research; SHEN Pei-ping (1964-), female, native of Nanyang, Henan, professor of North China University of Water Resources and Electric Power, Ph.D, engages in optimisation theory and applicatio; ZHONG Zhe-wei (2000-), male, native of Hangzhou, Zhejiang, master student of North China University of Water Resources and Electric Power, mainly engages in optimization theory and application research.
  • 基金资助:
    Supported by the National Natural Science Foundation of China (Grant Nos. 12571317 and 12071133).

Global Optimization Algorithm for Minimizing Linear Fractional Programming

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
  • Received:2025-04-07 Online:2026-03-30 Published:2026-03-30
  • About author:ZHAO Peng (2000-), male, native of Xinxiang, Henan, master student of North China University of Water Resources and Electric Power, engages in optimization theory and application research; SHEN Pei-ping (1964-), female, native of Nanyang, Henan, professor of North China University of Water Resources and Electric Power, Ph.D, engages in optimisation theory and applicatio; ZHONG Zhe-wei (2000-), male, native of Hangzhou, Zhejiang, master student of North China University of Water Resources and Electric Power, mainly engages in optimization theory and application research.
  • Supported by:
    Supported by the National Natural Science Foundation of China (Grant Nos. 12571317 and 12071133).

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摘要： In this paper, we study a class of Linear Fractional Programming on a nonempty bounded set, called the Problem (LFP), and design a branch and bound algorithm to find the global optimal solution of the problem (LFP). First, we convert the problem (LFP) to the equivalent problem (EP2). Secondly, by applying the linear relaxation technique to the problem (EP2), the linear relaxation programming problem (LRP2Y ) was obtained. Then, the overall framework of the algorithm is given, and the convergence and complexity of the algorithm are analyzed. Finally, experimental results are listed to illustrate the effectiveness of the algorithm.

关键词: Global optimization, Linear Fractional Programming, Branch and bound algorithm, Linear relaxation

Abstract: In this paper, we study a class of Linear Fractional Programming on a nonempty bounded set, called the Problem (LFP), and design a branch and bound algorithm to find the global optimal solution of the problem (LFP). First, we convert the problem (LFP) to the equivalent problem (EP2). Secondly, by applying the linear relaxation technique to the problem (EP2), the linear relaxation programming problem (LRP2Y ) was obtained. Then, the overall framework of the algorithm is given, and the convergence and complexity of the algorithm are analyzed. Finally, experimental results are listed to illustrate the effectiveness of the algorithm.

Key words: Global optimization, Linear Fractional Programming, Branch and bound algorithm, Linear relaxation

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