Are there examples where the typical "tight coupling" between a decision problem and the correponding optimization problem breaks down or behaves in an unusual way, e.g. have significantly different complexity?
Or, maybe there is a case where there is a cluster of problems that are all closely related, but the "best" or "definitive" version is not obvious or apparent? Also, I am looking for any survey or broad overview or discussion of this apparent basic connection between decision and optimization problems.
A similar question was asked here, but the answers were highly theoretical and it did not seem to yield any specific or tangible examples.