Is It Possible to Know a Problem Instance Is Ill-Posed?
James Renegar · Journal of Complexity · 1994
We develop some foundations for a general theory of condition numbers, ill-posed problem instances, and related concepts. Justification for our formalizations is provided by results from semi-algebraic geometry, with particular reliance on the fact that decision methods for the first-order theory of the reals exist, as was proven by Tarski.