Semi infinite programming

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In mathematics, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or a infinite number of variables and a finite number of constraints [1]. In the former case the constraints are typically parameterized by parameters.

1 Mathematical formulation of the problem
2 Methods for solving the problem
3 Examples
4 See also
5 References
6 External links

[edit] Mathematical formulation of the problem

The problem can be stated simply as:

$\min\limits_{x \in X}\;\; f(x)$

$\mbox{subject to: }\$

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

where

$f: R^n \to R$

$g: R^n \times R^m \to R$

$X \subseteq R^n$

$Y \subseteq R^m.$

SIP can be seen as a special case of bilevel programs (Multilevel programming) in which the lower-level variables do not participate in the objective function.

[edit] Methods for solving the problem

[edit] Examples

[edit] See also

optimization

[edit] References

Rembert Reemtsen and Jan-J. Rückmann (Editors), Semi-Infinite Programming (Nonconvex Optimization and Its Applications). Springer, 1998, ISBN 07923505451998