A review of complementarity problems for the design and analysis of infrastructure

Complementarity problems are a class of optimization problems which widely pervade infrastructure systems. Complementarity problems capture the concept of network and system equilibrium without the use of a mono-objective function. As a result these problems are useful for modeling infrastructure systems subject to use by actors with varied interests and objectives. Complementarity problems have been applied to both technical as well as economic systems. As such complementarity problems are particularly well-suited for modeling mixed or socio-technical systems. This paper provides a brief tutorial on complementarity problems, reviews the application literature on these problems, provides a working example in the context of networked infrastructure, and concludes with an agenda for future research.