An outer space approximation approach for generalized affine multiplicative programming problems

• Published in: Advances in continuous and discrete models Vol. 2025; no. 1; p. 122
• Main Authors: Hou, Zhisong, Zhao, Zhenwei, Bai, Yupeng, Guo, Deke
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2025; Springer Nature B.V
• Subjects: Algorithms; Analysis; Approximation; Design; Difference and Functional Equations; Equivalence; Functional Analysis; Linear programming; Mathematics; Mathematics and Statistics; Optimization; Ordinary Differential Equations; Partial Differential Equations; Variables; Branch-and-bound; Global optimization; Parabolic approximation; Branch reduction; Generalized affine multiplicative programming
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-025-03981-1

This paper investigates generalized affine multiplicative programming problems (GAMPP) and proposes an efficient outer space approach for obtaining the global optimal solution. By transforming each affine function within the objective function of the GAMPP into a variable in outer space, the GAMPP is reformulated as an equivalent problem. Subsequently, the equivalent problem is relaxed into a series of linear relaxed problems, leveraging the properties of parabolic functions. Following the development of several branch reduction techniques, an outer space branch reduction bound algorithm is designed, which is based on the branch-and-bound framework and the relaxation methods. Additionally, the complexity of the proposed algorithm is analyzed alongside a convergence analysis. Finally, experimental results demonstrate the computational efficiency and robustness of the proposed algorithm.