@article{Zhang2024, 
author = {Bo Zhang and Yuelin Gao and Ying Qiao and Ying Sun},
title = {A nonlinear relaxation-strategy-based algorithm for solving sum-of-linear-ratios problems},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {25396-25412},
keywords = {global optimization, fractional program, branch and bound, SOCP relaxation},
url = {https://www.sciopen.com/article/10.3934/math.20241240},
doi = {10.3934/math.20241240},
abstract = {This paper mainly studies the sum-of-linear-ratios problems, which have important applications in finance, economy and computational vision. In this process, we first propose a new method to re-represent the original problem as an equivalent problem (EP). Secondly, by relaxing these constraints, a nonlinear relaxation subproblem is constructed for EP. In view of the special structure of the relaxation, it is reconstructed as a second-order cone programming (SOCP) problem, which is essentially a SOCP relaxation of EP. Thirdly, through the structural characteristics of the objective function of EP, a region reduction technique is designed to accelerate the termination of the algorithm as much as possible. By integrating the SOCP relaxation and acceleration strategy into the branch and bound framework, a new global optimization algorithm is developed. Further, the theoretical convergence and computational complexity of the algorithm are analyzed. Numerical experiment results reveal that the algorithm is effective and feasible.}
}