A new branch and bound algorithm for minimax ratios problems

• Main Authors: Zhao Yingfeng, Liu Sanyang, Jiao Hongwei
• Format: Article
• Language: English
• Published: De Gruyter 2017-06-01
• Series: Open Mathematics
• Subjects: fractional programming; global optimization; branch and bound; adapted ratio partition; 90c26; 90c30
• Online Access: https://doi.org/10.1515/math-2017-0072

This study presents an efficient branch and bound algorithm for globally solving the minimax fractional programming problem (MFP). By introducing an auxiliary variable, an equivalent problem is firstly constructed and the convex relaxation programming problem is then established by utilizing convexity and concavity of functions in the problem. Other than usual branch and bound algorithm, an adapted partition skill and a practical reduction technique performed only in an unidimensional interval are incorporated into the algorithm scheme to significantly improve the computational performance. The global convergence is proved. Finally, some comparative experiments and a randomized numerical test are carried out to demonstrate the efficiency and robustness of the proposed algorithm.