Generalized semi-infinite programming

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:

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

$\text{subject to: }$

$g(x,y)\le 0,\mathrm{\forall }y\in Y(x)$

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