An investigation of the linear three level programming problem
An investigation of the linear three level programming problem
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DOI：
10.1109/tsmc.1984.6313291
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
J. Bard
中科院分区：
文献类型：
--
作者：
J. Bard
开环Stackelberg游戏的概念扩展到p球员的多级规划问题（MLPP），因此可以作为一个模型的各种层次系统中，顺序规划是规范。首先给出了每个局中人的理性反应集，然后阐述了线性MLPP的几何性质。其次，一阶必要条件的推导，并作为一个标准的非线性规划问题重铸。提出了一种在每次迭代中使用顶点搜索过程的切割平面算法来解决线性三层情况。最后通过一个算例说明了结果，并附有沿着一些计算经验。
The open-loop Stackelberg game is conceptually extended to p players by the multilevel programming problem (MLPP) and can thus be used as a model for a variety of hierarchical systems in which sequential planning is the norm. The rational reaction sets for each of the players is first developed, and then the geometric properties of the linear MLPP are stated. Next, first-order necessary conditions are derived, and the problem is recast as a standard nonlinear program. A cutting plane algorithm using a vertex search procedure at each iteration is proposed to solve the linear three-level case. An example is given to highlight the results, along with some computational experience.