// Workers AI · dad joke modeWhat did generalized semi-infinite programming say? It had infinite problems.

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:

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

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

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

where

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

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

$X\subseteq R^{n}$

$Y\subseteq R^{m}.$

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

See also

• optimization
• Semi-Infinite Programming (SIP)

External links

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