# Generalized semi-infinite programming

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In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a **generalized semi-infinite programming** (**GSIP**) problem, the feasible set of the parameters depends on the variables.^{[1]}

## Mathematical formulation of the problem

The problem can be stated simply as:

where

In the special case that the set : is nonempty for all GSIP can be cast as bilevel programs (Multilevel programming).

## Methods for solving the problem

## Examples

## See also

## References

- ↑ O. Stein and G. Still,
*On generalized semi-infinite optimization and bilevel optimization*, European J. Oper. Res., 142 (2002), pp. 444-462