Some implementation issues associated with multidimensional interval Newton methods
Publication in refereed journal


香港中文大学研究人员 ( 现职)

陈伟光教授 (音乐系)

全文

数位物件识别号 (DOI) http://dx.doi.org/10.1007/BF02242020

引用次数
Web of Sciencehttp://aims.cuhk.edu.hk/converis/portal/Publication/1WOS source URL
Scopushttp://aims.cuhk.edu.hk/converis/portal/Publication/1Scopus source URL

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摘要This paper presents the development of an optimal interval Newton method for systems of nonlinear equations. The context of solving such systems of equations is that of optimization of nonlinear mathematical programs. The modifications of the interval Newton method presented in this paper provide computationally effective enhancements to the general interval Newton method. The paper demonstrates the need to compute an optimal step length in the interval Newton method in order to guarantee the generation of a sequence of improving solutions. This method is referred to as the optimal Newton method and is implemented in multiple dimensions. Secondly, the paper demonstrates the use of the optimal interval Newton method as a feasible direction method to deal with non-negativity constraints. Also, included in this implementation is the use of a matrix decomposition technique to reduce the computational effort required to compute the Hessian inverse in the interval Newton method. The methods are demonstrated on several problems. Included in these problems are mathematical programs with perturbations in the problem coefficients. The numerical results clearly demonstrate the effectiveness and efficiency of these approaches. ? http://aims.cuhk.edu.hk/converis/portal/Publication/199http://aims.cuhk.edu.hk/converis/portal/Publication/1 Springer-Verlag.

着者Dinkel J.J., Tretter M., Wong D.
期刊名称Computing
详细描述Paper presented in the 34th International Congress of Asian and North African Studies, organized by University of Hong Kong
出版年份http://aims.cuhk.edu.hk/converis/portal/Publication/199http://aims.cuhk.edu.hk/converis/portal/Publication/1
月份3
日期http://aims.cuhk.edu.hk/converis/portal/Publication/1
卷号47
期次http://aims.cuhk.edu.hk/converis/portal/Publication/1
出版社Springer Verlag
出版地Germany
页次29 - 42
国际标準期刊号00http://aims.cuhk.edu.hk/converis/portal/Publication/10-485X
语言英式英语

关键词AMS subject Classification: 65K05, interval arithmetic, Interval Newton method, optimization