# Generalized semi-infinite programming

Generalized semi-infinite programming

In mathematics, generalized semi-infinite programming (GSIP) is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are parameterized by parameters and the feasible set of the parameters depends on the variables.

Mathematical formulation of the problem

The problem can be stated simply as::$minlimits_\left\{x in X\right\};; f\left(x\right)$

:$mbox\left\{subject to: \right\}$

::$g\left(x,y\right) le 0, ;; forall y in Y\left(x\right)$

where:$f: R^n o R$:$g: R^n imes R^m o R$:$X subseteq R^n$:$Y subseteq R^m.$

In the special case that the set :$Y\left(x\right)$ is nonempty for all $x in X$ GSIP can be cast as bilevel programs (Multilevel programming).

Methods for solving the problem

Examples

* optimization
* SIP

References

* [http://glossary.computing.society.informs.org/ Mathematical Programming Glossary]

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