Misplaced Pages

Generalized semi-infinite programming

Article snapshot taken from[REDACTED] with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "Generalized semi-infinite programming" – news · newspapers · books · scholar · JSTOR (May 2008) (Learn how and when to remove this message)

In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a generalized semi-infinite programming (GSIP) problem, the feasible set of the parameters depends on the variables.

Mathematical formulation of the problem

The problem can be stated simply as:

min x X f ( x ) {\displaystyle \min \limits _{x\in X}\;\;f(x)}
subject to:    {\displaystyle {\mbox{subject to: }}\ }
g ( x , y ) 0 , y Y ( x ) {\displaystyle g(x,y)\leq 0,\;\;\forall y\in Y(x)}

where

f : R n R {\displaystyle f:R^{n}\to R}
g : R n × R m R {\displaystyle g:R^{n}\times R^{m}\to R}
X R n {\displaystyle X\subseteq R^{n}}
Y R m . {\displaystyle Y\subseteq R^{m}.}

In the special case that the set : Y ( x ) {\displaystyle Y(x)} is nonempty for all x X {\displaystyle x\in X} GSIP can be cast as bilevel programs (Multilevel programming).

Methods for solving the problem

This section is empty. You can help by adding to it. (July 2010)

Examples

This section is empty. You can help by adding to it. (July 2010)

See also

References

  1. O. Stein and G. Still, On generalized semi-infinite optimization and bilevel optimization, European J. Oper. Res., 142 (2002), pp. 444-462

External links

Category:
Generalized semi-infinite programming Add topic