Semi-infinite programming

This article is an orphan, as few or no other articles link to it. Please introduce links to this page from other articles related to it. (February 2009)

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (May 2008)

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.

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

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.

Methods for solving the problem

Examples

References

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