摘要
考虑非线性规划以及这里Ａ为ｍ×ｎ阶矩阵，ｃｉ，ｄ，ｘ∈Ｒｎ，ｂ∈Ｒｍ，ｒ＞０．我们假定ｘ∈Ｄ（（ＮＬＰⅠ）的可行域）有ｃ＇ｉｘ＞０，ｉ＝１，．．．，ｈ．利用算术－几何平均值不等式将（ＮＬＰⅠ）转化为参数线性规划，证明参数只须取一些特定的值，并且它的最优解在Ｄ的顶点处实现，对于（ＮＬＰⅡ）也将得到类似结果．
The non-linear programmings and are concidered, where A is a m × n-matrix, ci, d,x∈6 Rn, b ∈ Rm, and x> 0,i = 1, ..,k, x> D(the feasible region of (NLP Ⅰ )). By means of the arithmetic-geometric means inequality, it is shown that (NLP Ⅰ ) can be converted into a parametric linear programming,and the parameters are needed only to take special values. The similar results are obtained for (NLP Ⅱ ).
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
1996年第6期736-739,共4页
Journal of Inner Mongolia University：Natural Science Edition
基金
内蒙古自然科学基金
关键词
非线性规划
几何平均值
不等式
算术平均值
non-linear programming parametric linear programming arithmetic-geometric means inequality
