A new branch and bound algorithm for minimax ratios problems

Yingfeng 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 -