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

Hongwei Jiao; Sanyang Liu; Jingben Yin; Yingfeng Zhao

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 736-746
- ISSN: 2391-5455

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topHongwei Jiao, et al. "Outcome space range reduction method for global optimization of sum of affine ratios problem." Open Mathematics 14.1 (2016): 736-746. <http://eudml.org/doc/287130>.

@article{HongweiJiao2016,

abstract = {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 part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.},

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

journal = {Open Mathematics},

keywords = {Range reduction method; Global optimization; Sum of affine ratios; Linear relaxation program; Branch-and-bound; range reduction method; global optimization; sum of affine ratios; linear relaxation program; branch-and-bound},

language = {eng},

number = {1},

pages = {736-746},

title = {Outcome space range reduction method for global optimization of sum of affine ratios problem},

url = {http://eudml.org/doc/287130},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Hongwei Jiao

AU - Sanyang Liu

AU - Jingben Yin

AU - Yingfeng Zhao

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

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 736

EP - 746

AB - 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 part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.

LA - eng

KW - Range reduction method; Global optimization; Sum of affine ratios; Linear relaxation program; Branch-and-bound; range reduction method; global optimization; sum of affine ratios; linear relaxation program; branch-and-bound

UR - http://eudml.org/doc/287130

ER -

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