Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities

disjunctions of constraints of the form "there exist y1,...,yn
s.t. f=0 and g1>=0 and ... and gk>= 0" in additional free
variables, terminating for all cases when this results in a
numerically well-posed problem. The only assumption on the
terms f, g1,..., gn is the existence of a pruning function,
as given by constraint propagation algorithms or by interval
arithmetic. To the best of my knowledge this is the first
algorithm for solving such constraints.