The basic tool in the verified solution of constrained or unconstrained optimization or root-finding problems is the interval Newton method. Analogues of conventional termination criteria can be problematic, potentially leading to inadequate answers or major inefficiencies. The authors illustrate some of the pitfalls and propose a new “thickness stopping criterion.” They sketch the logic of a parameterized family of criteria, which can be adapted to varying user needs in particular problem contexts, and discuss a nontrivial example. Evaluation must await extensive experimentation.

Overall, the paper is well written, but appreciation of some details requires familiarity with existing codes and prior literature cited therein.