Semi infinite programming

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 [http://glossary.computing.society.informs.org/second.php?page=S.html#Semi-infinite_program] . In the former case the constraints are typically parameterized.

Mathematical formulation of the problem

The problem can be stated simply as::$minlimits\_\{x\; in\; X\};;\; f(x)$

:$mbox\{subject\; to:\; \}$

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

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

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

See also

* optimization

References

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

External links

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