线性规划问题的多重解及其寻求  

Multivalued solution of linear program and the way to find it

作　　者：叶秉如[1] 董增川[1] 许静仪[1] 陈乐湘[1] 叶宇达[2] 

机构地区：[1]河海大学水资源环境学院,江苏南京210098 [2]南京大学现代分析中心,江苏南京210093

出　　处：《河海大学学报（自然科学版）》2005年第2期224-231,共8页Journal of Hohai University(Natural Sciences)

摘　　要：利用线性规划新解法———分解筛选法的解题特点,对线性规划实际存在的多重解问题进行分析,提出了多重解的两大类型,即相似性重解(又称重解Ⅰ型)和无关性重解(又称重解Ⅱ型),研究了它们产生的充要条件,特别是研究了这两类多重解通解(generalsolution)的求解方法和一些相应的算例,并对多重解实际应用上的重要之处进行了扼要论述.Based on the new method, named the decomposition-screening method, for solving the linear program problem, a detailed analysis was made on the multivalued solution to linear program. Two kinds of multivalued solutions were identified, i.e. the multivalued solution of similar type and the multivalued solution of unrelated type, and the necessary and sufficient conditions for their existence were discussed. Furthermore, the way to find the general solution of the two kinds of multivalued solutions was given together with some interesting examples of each type, and some key points of the multivalued solution in practical application were also briefly discussed.

关 键 词：线性规划 多重解 通解 

分 类 号：O151.2[理学—数学]