Global Optimization of a Class of Radical FunctionsUsing a Symbolic Algorithm

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Global Optimization of a Class of Radical FunctionsUsing a Symbolic Algorithm

更新时间：2023-11-28

- Global Optimization of a Class of Radical FunctionsUsing a Symbolic Algorithm
- Advanced Engineering Sciences Vol. 40, Issue 6, Pages: 140-143(2008)
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- Published：2008，
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徐嘉.一类根式型函数全局优化的符号算法[J].工程科学与技术,2008,40(6):140-143.

Global Optimization of a Class of Radical FunctionsUsing a Symbolic Algorithm. [J]. Advanced Engineering Sciences 40(6):140-143(2008)
徐嘉.一类根式型函数全局优化的符号算法[J].工程科学与技术,2008,40(6):140-143. DOI：

Global Optimization of a Class of Radical FunctionsUsing a Symbolic Algorithm. [J]. Advanced Engineering Sciences 40(6):140-143(2008) DOI：

摘要

中文摘要: 为了提高形如g=m1u1+m2u2+…+mnun的根式型函数全局优化算法的效率

从根式型函数的有理化入手

讨论了这类根式型函数不等式成立的充要条件。这一充要条件成功地将形如上式的根式型不等式等价转化成了一组有理不等式。将这一条件用于此类根式型函数全局优化的符号算法中

有效地改进了原有的通用算法

从而达到了提高原算法在此类根式型函数上运算效率的目的。

Abstract

Abstract:The necessary and sufficient condition for a class of inequalities with radical functions like g=m1u1+m2u2+…+mnun was discussed based on the rationalization of radical functions. This condition successfully transformed the inequality with radical functions into a set of rational inequalities. Furthermore

the condition was applied to symbolic algorithm of global optimization of the class of radical functions. Thus

the former universal algorithm was improved so that the new algorithm is much more efficient.

关键词

全局优化符号算法根式函数差分代换

Keywords

global optimizationsymbolic algorithmradical functionssds

references

杨路,全局优化的符号算法与有限核原理,济南:山东教育出版社,2001.

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杨路不等式机器证明的降维算法与通用程序 [J].

Yang Lu,Practical automated reasoning on inequalities:Generic programs for inequality proving and discovering,Springer-verlag,1998.

夏时洪一类不等式型定理可读证明的自动生成 [D].2002

杨路.夏时洪一类构造性几何不等式的机器证明 [J].

匡继昌,常用不等式,长沙:湖南教育出版社,2004.

单墫,几何不等式在中国,南京:江苏教育出版社,1996.

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