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A new branch and bound algorithm for minimax ratios problems

Yingfeng Zhao;  Sanyang Liu;  Hongwei Jiao — 2017

Open Mathematics

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...

Outcome space range reduction method for global optimization of sum of affine ratios problem

Hongwei Jiao;  Sanyang Liu;  Jingben Yin;  Yingfeng Zhao — 2016

Open Mathematics

Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large...

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