Complexity analysis of a semi-infinite optimization problem in interval arithmetic
Many problems in interval arithmetic in a natural way lead to
a quantifier elimination problem over the reals.
By studying closer the precise form of the latter we show that
in some situations it is possible to obtain a refined
complexity analysis of the problem.
This is done by structural considerations of the special form of the quantifiers
and its implications for the analysis in a real number model
of computation. Both can then be used to obtain as well new results in the
Turing model. We exemplify our approach by dealing with a semi-infinite