Generalized semi-infinite programming Source: en.wikipedia.org/wiki/Generalized_semi-infinite_programming

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.^[1]

The problem can be stated simply as:

${\displaystyle \min \limits _{x\in X}\;\;f(x)}$

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

${\displaystyle g(x,y)\leq 0,\;\;\forall y\in Y(x)}$

where

${\displaystyle f:R^{n}\to R}$

${\displaystyle g:R^{n}\times R^{m}\to R}$

${\displaystyle X\subseteq R^{n}}$

${\displaystyle Y\subseteq R^{m}.}$

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

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

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

• optimization
• Semi-Infinite Programming (SIP)

• Mathematical Programming Glossary Archived 2010-03-28 at the Wayback Machine