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\begin{align}
J^*(\theta) = & \min_{x\in\mathbb R^n}\; f(x,\theta) \\
& g(x,\theta)\leq 0, \\
& \theta \in \Theta \subset R^m
\end{align}
</math>
where <math>x</math> is the optimization variable, <math>\theta
== Classification ==
Depending on the nature of <math>f(x,\theta)</math> and <math>g(x,\theta)</math> and whether the optimization problem features integer variables, parametric programming problems are classified into different sub-classes:
* If more than one parameter is present, i.e. <math>m > 1</math>, then it is often referred to as multiparametric programming problem
* If integer variables are present, then the problem is referred to as (multi)parametric mixed-integer programming problem
* If constraints are linear, then additional classifications depending to nature of the objective function in (multi)parametric (mixed-integer) linear, quadratic and nonlinear programming problems is performed. Note that this generally assumes the constraints to be affine.
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