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.

Mathematical formulation of the problem

The problem can be stated simply as:

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

$\text{subject to: }$

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

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)

External links

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