Constrained mixed-integer transfer conjecture

Let $\ell$ be a lower bound on the information complexity, with respect to a fixed oracle, for a family of continuous, constrained convex optimization instances. Mixed-integer transfer conjecture. If such a family exists, then for every $n\geq 1$ there exist mixed-integer instances with $n$ integer variables whose information complexity, with respect to the same oracle, is lower bounded by

$$\Omega(2^n\cdot\ell).$$

This would extend the paper's pure-optimization transfer theorem to constrained problems and would yield the stated feasibility-based mixed-integer lower bounds as a special case. It would also transfer future improved feasibility lower bounds for continuous convex optimization to the mixed-integer setting.