We analyze the question of deciding whether a quadratic or a hyperbolic 0-1 programming instance has a unique optimal solution. Both uniqueness questions are known to be NP-hard, but are unlikely to be contained in the class NP. We precisely pinpoint their computational complexity by showing that they both are complete for the complexity class $\Delta_2 P$ .
Deineko, V. G., Klinz, B., & Woeginger, G. J. (2013). Uniqueness in quadratic and hyperbolic 0-1 programming problems. Operations Research Letters, 41(6), 633-635. https://doi.org/10.1016/j.orl.2013.08.013