An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems

Hongwei Jiao (), Binbin Li () and Youlin Shang ()
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Hongwei Jiao: Henan Institute of Science and Technology
Binbin Li: Henan Institute of Science and Technology
Youlin Shang: Henan University of Science and Technology

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 1, 35 pages

Abstract: Abstract This paper aims to globally solve a generalized affine fractional program problem (GAFPP). Firstly, by introducing some outer space variables and performing equivalent transformations, we can derive the equivalence problem (EP) of the GAFPP. Secondly, by constructing a novel linear relaxation method, we can deduce the affine relaxation problem (ARP) of the EP. Next, by solving the ARP to compute the lower bound, we propose a new outer space branch-and-bound algorithm for tackling the GAFPP. Then, the global convergence of the algorithm is proved, and the computational complexity of the algorithm in the worst case is analyzed. Finally, numerical experimental results are reported to illustrate the effectiveness of the algorithm.

Keywords: Generalized affine fractional program; Global optimization; Affine relaxation problem; Outer space approach; Computational complexity; 90C32; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02368-0

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