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A new branch and bound algorithm for minimax ratios problems

Yingfeng ZhaoSanyang LiuHongwei 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...

Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

Zhisong HouHongwei JiaoLei CaiChunyang Bai — 2017

Open Mathematics

This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without...

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

Hongwei JiaoSanyang LiuJingben YinYingfeng 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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