The trouble with the second quantifier

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.

Automated summary

This paper explores optimization problems with natural formulations using existential and universal quantifiers. Theoretical background from computational complexity theory and numerous illustrating examples are presented. Connections to robust optimization and bilevel optimization are discussed, along with reasons for why the operational research community should be interested in the theoretical aspects of this field.