灰色正项几何规划研究

数学季刊 ›› 2005, Vol. 20 ›› Issue (1): 34-41.

灰色正项几何规划研究

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; Department of Mathematics, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008, China

收稿日期:2004-02-12 出版日期:2005-03-30 发布日期:2024-01-26
作者简介:LUO Dang(1959-),male,native of Runan,Henan,an associate professor of North China Insti- tute of Water Conservancy and Hydroelectric Power,Ph.D.,engages in grey system theory,system engineering, etc.
基金资助:
Supported by the NSF Jiangsu Province(BK2003211) Supported by the NSF of Henan Province(2003120001)；

Study on the Grey Polynomial Geometric Programming

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; Department of Mathematics, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008, China

Received:2004-02-12 Online:2005-03-30 Published:2024-01-26
About author:LUO Dang(1959-),male,native of Runan,Henan,an associate professor of North China Insti- tute of Water Conservancy and Hydroelectric Power,Ph.D.,engages in grey system theory,system engineering, etc.
Supported by:
Supported by the NSF Jiangsu Province(BK2003211) Supported by the NSF of Henan Province(2003120001)；

摘要/Abstract

摘要： In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θpositioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.

关键词: interval grey numbers, grey polynomial geometric programming, θ positioned geometric programming, algorithm

Abstract: In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θpositioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.

Key words: interval grey numbers, grey polynomial geometric programming, θ positioned geometric programming, algorithm

中图分类号:

O221

罗党. 灰色正项几何规划研究[J]. 数学季刊, 2005, 20(1): 34-41.

LUO Dang. Study on the Grey Polynomial Geometric Programming[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(1): 34-41.

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