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Solving interval linear programming problems with equality constraints using extended interval enclosure solutions

机译:使用扩展间隔机柜解决方案解决与平等约束的间隔线性编程问题

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This paper focuses on solving systems of interval linear equations and interval linear programming in a computationally efficient way. Since the computational complexity of most interval enclosure numerical methods is often prohibitive, a procedure to obtain a relaxation of the interval enclosure solution that is computationally tractable is proposed. We show that our approach unifies the four standard interval solutions-the weak, strong, control and tolerance solutions. The interval linear system methods require n2n linear solutions. However, in the case of linear programming problems, we show that this requires just two optimization problem of the size of the problem itself. Numerical examples illustrate our results.
机译:本文以计算有效的方式侧重于求解间隔线性方程和间隔线性规划系统。 由于大多数间隔内尺的计算复杂性通常是禁止的,因此提出了一种用于在计算上易于计算的间隔外壳解决方案的放松的过程。 我们表明我们的方法统一了四个标准间隔解决方案 - 弱,强,控制和公差解决方案。 间隔线性系统方法需要N2N线性解决方案。 但是,在线性编程问题的情况下,我们表明这只需要两个优化问题的问题本身。 数值例子说明了我们的结果。

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