区间线性规划问题的强无界性

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI:10.1109/SCAN.2006.42

J. Koničková

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引用次数: 7

摘要

如果在区间内固定系数得到的线性规划问题是无界的，则系数由区间规定的线性规划问题称为强无界线性规划问题。在本文的主要结果中，给出了一类区间线性规划问题强无界性的一个充要条件。为了有一个全貌，我们还给出了该问题具有强可行性和强可解性的条件。通过有限算法的适当性质检验，验证了强可行性、强可解性和强无界性的充分必要条件。检验强可行性和检验强可解性是np困难的。我们证明了检验强无界性也是np困难的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Strong Unboundedness of Interval Linear Programming Problems

A linear programming problem whose coefficients are prescribed by intervals is called strongly unbounded if each linear programming problem obtained by fixing coefficients in these intervals is unbounded. In the main result of this paper a necessary and sufficient condition for strong unboundedness of an interval linear programming problem is described. In order to have a full picture we also show conditions for strong feasibility and strong solvability of this problem. The necessary and sufficient conditions for strong feasibility, strong solvability and strong unboundedness can be verified by checking the appropriate properties by the finite algorithms. Checking strong feasibility and checking strong solvability are NP-hard. We show that checking strong unboundedness is NP-hard as well.

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12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)

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