Semi-infinite Programming

In optimization theory, 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. In the former case the constraints are typically parameterized.
*
* M. A. Goberna and M. A. López, ''Linear Semi-Infinite Optimization'', Wiley, 1998.
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Mathematical formulation of the problem

The problem can be stated simply as:
:$\min_\;\; f(x)$

:$\text$

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

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 in which the lower-level variables do not participate in the objective function.

Methods for solving the problem

In the meantime, see external links below for a complete tutorial.

Examples

In the meantime, see external links below for a complete tutorial.

See also

* Optimization
* Generalized semi-infinite programming (GSIP)

References

* Edward J. Anderson and Peter Nash, ''Linear Programming in Infinite-Dimensional Spaces'', Wiley, 1987.
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* M. A. Goberna and M. A. López, ''Linear Semi-Infinite Optimization'', Wiley, 1998.
*
* David Luenberger (1997). ''Optimization by Vector Space Methods.'' John Wiley & Sons. .
* Rembert Reemtsen and Jan-J. Rückmann (Editors), ''Semi-Infinite Programming (Nonconvex Optimization and Its Applications)''. Springer, 1998, , 1998

External links

Description of semi-infinite programming from INFORMS (Institute for Operations Research and Management Science)


A complete, free, open source Semi Infinite Programming Tutorial is available here from Elsevier as a pdf download from their Journal of Computational and Applied Mathematics, Volume 217, Issue 2, 1 August 2008, Pages 394–419

Optimization in vector spaces
Approximation theory
Numerical analysis

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