The trouble with the second quantifier - Gerhard J. Woeginger (4OR, 2021)
We survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.
Keywords: 330; Combinatorial optimization; Complexity theory; Polynomial hierarchy; Bilevel optimization