keynote:lesson13
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| 若${\bar {\mathbf b}}\geq{\mathbf 0}$，则式$(2)$就对应着基本可行解${\bar {\mathbf x}}= | 若${\bar {\mathbf b}}\geq{\mathbf 0}$，则式$(2)$就对应着基本可行解${\bar {\mathbf x}}= | ||
| \begin{pmatrix} | \begin{pmatrix} | ||
| - | {\bar {\mathbf b}}\\ | + | {\bar {\mathbf b}}\newline |
| {\mathbf 0}\\ | {\mathbf 0}\\ | ||
| \end{pmatrix} | \end{pmatrix} | ||
| Line 316: | Line 316: | ||
| =====2.6修改单纯形法===== | =====2.6修改单纯形法===== | ||
| + | **当LP问题的规模很大时，如何减少存储量和计算时间，就是一个必须加以考虑的问题。在实际中，大多采用修改单纯形法。** | ||
| - | + | ---- | |
| - | + | **逆矩阵法** | |
| - | + | 一般单纯形表为\\ | |
| - | <note important>高海东 2010/06/17</note> | + | {{:keynote:一般单纯形表.jpg|}} \\ |
| + | 逆矩阵法对每一张单纯形表，仅存贮下列数据 \\ | ||
| + | {{:keynote:修改单纯形表.jpg|}} \\ | ||
| + | 上表称为修改单纯形表。 \\ | ||
| + | 根据这张表和原始数据进行迭代计算。由$ζ_k = \max\{ {\mathbf w}{\mathbf a}_j - c_j|x_j非基变量 \}$确定$x_k$为进基变量，再求${\bar {\mathbf a}}_k = B^{-1} {\mathbf a}_k$，用最小比确定离基变量$x_r$，得到新的基$\hat B$，最后构造对应于$\hat B$的修改单纯形表。如果每一次迭代都必须重构造$B^{-1}$，则计算量显然难以令人满意。\\ | ||
| + | 定理：对应基$B$的修改单纯形表的右边添加一列$\begin{pmatrix} ζ_k \newline {\bar {\mathbf a}}_k \end{pmatrix}$，以${\bar {\mathbf a}}_{rk}$为转轴元旋转，就得到了对应于基$\hat B$的修改单纯形表。 | ||
| + | <note important> --- //[[1@1|高海东]] 2010/06/24 22:07//</note> | ||
keynote/lesson13.txt · Last modified: 2023/08/19 21:02 (external edit)
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