Solving generalized polynomial problem by using new affine relaxed technique

被引:26
作者
Jiao, Hongwei [1 ,2 ]
Shang, Youlin [2 ]
Wang, Wenjie [1 ]
机构
[1] Henan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R China
[2] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China
基金
中国国家自然科学基金; 中国博士后科学基金;
关键词
Generalized polynomial problem; fractional programming; global optimization; affine relaxed technique; branch-and-bound; GLOBAL OPTIMIZATION; BOUND ALGORITHM; SUM; NONCONVEX; BRANCH;
D O I
10.1080/00207160.2021.1909727
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article presents and validates a new branch-and-bound algorithm for effectively solving the generalized polynomial problem (GPP). In this algorithm, a new affine relaxed technique is derived for establishing the relaxed linear programs problem of the GPP. In addition, some box reducing manipulations are employed to improve the speed of branch-and-bound search of the algorithm. Combining the relaxed linear programs problem with the box reducing manipulations, a new branch-and-bound algorithm is constructed. Some numerical examples are solved to verify the potential practical and computing advantages of the algorithm. At last, several engineering design problems are solved to validate the usefulness of the algorithm.
引用
收藏
页码:309 / 331
页数:23
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