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›› 2015, Vol. 32 ›› Issue (5): 577-581.DOI: 10.7523/j.issn.2095-6134.2015.05.001

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A further discussion on the conservatism of robust linear optimization problems

LIU Pengfei1,2, YANG Wenguo1,2   

  1. 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
  • Received:2015-01-19 Revised:2015-04-14 Online:2015-09-15
  • Supported by:

    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.

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.

Key words: robust approach, conservatism, linear programming, distribution

CLC Number: