| 对鲁棒线性规划保守性的进一步讨论 |
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| 作者姓名： | 刘鹏飞 杨文国 |
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| 作者单位： | 1. 中国科学院大学数学科学学院, 北京 100049;
2. 中国科学院大数据挖掘与知识管理重点实验室, 北京 100049 |
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| 基金项目： | Supported by National 973 Plan Project(2011CB706900), 863 Plan Project(2011AA01A102), NSFC(71171189, 11331012, 71271204, and 11101420), the "Strategic Priority Research Program" of Chinese Academy of Sciences (XDA06010302), and the Open Preject of Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences and Huawei Technology Co., Ltd. |
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| 摘 要： | 保守性是衡量鲁棒优化模型好坏的重要指标,也是研究鲁棒优化方法的一个关键问题.在先前关于鲁棒线性优化保守性的研究中,我们发现,线性规划最优解中非零分量的数目k是刻画鲁棒线性规划模型保守性的一个重要参数.本文通过分析基解是鲁棒线性规划问题最优解的概率,给出了参数k的概率分布和数学期望.
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| 关 键 词： | 鲁棒方法 保守性 线性规划 分布 |
| 收稿时间： | 2015-01-19 |
| 修稿时间： | 2015-04-14 |
A further discussion on the conservatism of robust linear optimization problems |
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| Authors: | LIU Pengfei YANG Wenguo |
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| Institution: | 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
2. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | The conservatism is an important indicator for measuring a robust approach. In the process of our previous research for the conservatism of robust linear programming problems, we have found that k is a critical parameter to depict the conservatism of robust linear programming problems, where k is the number of nonzero components in optimal solution of the extremely conservative robust linear programming problems. In this paper we give the distribution and expectation of k through analyzing the probability that any basic solutions are the optimal solutions of the extremely conservative robust linear programming problems. |
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| Keywords: | robust approach conservatism linear programming distribution |
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