Parametric programming

Parametric programming is a type of mathematical optimization, where the optimization problem is solved as a function of one or multiple parameters. Developed in parallel to sensitivity analysis, its earliest mention can be found in a thesis from 1952. Since then, there have been considerable developments for the cases of multiple parameters, presence of integer variables as well as nonlinearities. In particular the connection between parametric programming and model predictive control established in 2000 has contributed to an increased interest in the topic.

In general, the following optimization problem is considered

where ${\displaystyle x}$ is the optimization variable, ${\displaystyle \theta }$ are the parameters, ${\displaystyle f(x,\theta )}$ is the objective function and ${\displaystyle g(x,\theta )}$ denote the constraints. Note that the space ${\displaystyle \Theta }$ is generally referred to as parameter space.

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