# A new branch and bound algorithm for minimax ratios problems

Yingfeng Zhao; Sanyang Liu; Hongwei Jiao

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 840-851
- ISSN: 2391-5455

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topYingfeng Zhao, Sanyang Liu, and Hongwei Jiao. "A new branch and bound algorithm for minimax ratios problems." Open Mathematics 15.1 (2017): 840-851. <http://eudml.org/doc/288305>.

@article{YingfengZhao2017,

abstract = {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.},

author = {Yingfeng Zhao, Sanyang Liu, Hongwei Jiao},

journal = {Open Mathematics},

keywords = {Fractional programming; Global optimization; Branch and bound; Adapted ratio partition},

language = {eng},

number = {1},

pages = {840-851},

title = {A new branch and bound algorithm for minimax ratios problems},

url = {http://eudml.org/doc/288305},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Yingfeng Zhao

AU - Sanyang Liu

AU - Hongwei Jiao

TI - A new branch and bound algorithm for minimax ratios problems

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 840

EP - 851

AB - 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.

LA - eng

KW - Fractional programming; Global optimization; Branch and bound; Adapted ratio partition

UR - http://eudml.org/doc/288305

ER -

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