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On 04/25/2012 07:11 PM, Dan Zuras Intervals wrote:
754 discussions (largely via the means of the spoken word) did not have much to do with the notion of an overflow as a way of dealing with infinity. In spite of the fact that it IS, in fact, the most common way of arriving at infinity on any computer I have ever had access to.
A very important way infinite bounds arise in applications of interval arithmetic to optimization problems is that a user specifies an inequality x>=0 for a variable but no upper bound. This means that x in [0,Inf], without any connection to overflow. Such specifications are very common, already for linear programs, which very often has unbounded variables. The reliable linear programming software of Cristian Jansson takes this into account, using sophisticated interval analysis to treat unbounded intervals correctly.
If this usage of unbounded intervals is not supported by the future standard, its usefulness in global optimization will be much limited.
Arnold Neumaier