Semi-infinite programming: Difference between revisions

Revision as of 02:24, 26 July 2010

Revision as of 10:34, 25 September 2010

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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 an 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:

:<math> \min\limits_{x \in X}\;\; f(x) </math>

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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 ==

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==Examples==

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== See also ==

* [[optimization (mathematics)|Optimization]]

* [[Generalized semi-infinite programming|Generalized semi-infinite programming (GSIP)]]

== 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]

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