A guided tour through the zoo of paired optimization problems

Abstract Many mathematical models are based on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle problems, standard and generalized semi-infinite problems, robust optimization, Lagrange duality, bicriteria optimization problems, minimax problems, decomposition, and two-stage stochastic optimization. Some connections to vector optimization and variational inequalities are discussed as well.