On multi-parametric programming and its applications in process systems engineering

•Comprehensive review of the developments in multi-parametric programming over the last 20 years.•Detailed description of applications beyond explicit model predictive control.•Opinionated view of future developments within multi-parametric programming and its applications. In multi-parametric programming, an optimization problem is solved for a range and as a function of multiple parameters. In this review, we discuss the main developments of multi-parametric programming over the last two decades from a theoretical, algorithmic and application perspective. In addition, we provide an opinionated view of the future research directions in multi-parametric programming.