Abstract
In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in ∑∀∃([A], [b]) = {x ∈ Rn | ∀A ∈ [A], ∃b ∈ [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in ∑∀∃([A], [b]), and we provide a new definition of the optimality of an interval vector included in ∑∀∃([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in ∑∀∃([A], [b]).
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Beaumont, O., Philippe, B. Linear Interval Tolerance Problem and Linear Programming Techniques. Reliable Computing 7, 433–447 (2001). https://doi.org/10.1023/A:1014758201565
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DOI: https://doi.org/10.1023/A:1014758201565