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} | ||
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| ===== 3.3对偶单纯形法 ===== | ===== 3.3对偶单纯形法 ===== | ||
| + | （Dual Simplex Method）1954年美国数学家C.莱姆基提出对偶单纯形法。单纯形法是从原始问题的一个可行解通过迭代转到另一个可行解，直到检验数满足最优性条件为止。对偶单纯形法则是从满足对偶可行性条件出发通过迭代逐步搜索原始问题的最优解。在迭代过程中始终保持基解的对偶可行性，而使不可行性逐步消失。设原始问题为min{cx|Ax=b，x≥0}，则其对偶问题（Dual Problem）为 max{yb|yA≤c}。当原始问题的一个基解满足最优性条件时,其检验数cBB-1A-c≤0。即知y＝cBB-1（称为单纯形算子）为对偶问题的可行解。所谓满足对偶可行性，即指其检验数满足最优性条件。因此在保持对偶可行性的前提下，一当基解成为可行解时，便也就是最优解。 | ||
| ===== 3.4原始-对偶单纯形法 ===== | ===== 3.4原始-对偶单纯形法 ===== | ||
keynote/lesson13.txt · Last modified: 2023/08/19 21:02 (external edit)
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