A Novel Affine Relaxation-Based Algorithm for Minimax Affine Fractional Program

Hongwei Jiao, Binbin Li () and Youlin Shang ()
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Hongwei Jiao: School of Mathematical Sciences, Henan Institute of Science and Technology, Hualan Street, Henan, Xinxiang 453003, P. R. China
Binbin Li: School of Mathematical Sciences, Henan Institute of Science and Technology, Hualan Street, Henan, Xinxiang 453003, P. R. China
Youlin Shang: School of Mathematics and Statistics, Henan University of Science and Technology, Kaiyuan Street, Henan, Luoyang 471023, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 05, 1-25

Abstract: This paper puts forward a novel affine relaxation-based algorithm for solving the minimax affine fractional program problem (MAFPP) over a polyhedron set. First of all, some new variables are introduced for deriving the equivalence problem (EP) of the MAFPP. Then, for the EP, the affine relaxation problem (ARP) is established by using the two-stage affine relaxation method. The method provides a lower bound by solving the ARP in the branch-and-bound searching process. By subdividing the output space rectangle and solving a series of ARPs continuously, the feasible solution sequence generated by the algorithm converges to a global optimal solution of the initial problem. In addition, the algorithmic maximum iteration in the worst case is estimated by complexity analysis for the first time. Lastly, the practicability and effectiveness of the algorithm have been verified by numerical experimental results.

Keywords: Minimax affine fractional program; affine relaxation-based algorithm; two-stage affine relaxation method; output space branch-and-bound; complexity analysis (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500367

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