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

Mathematical formulation of the problem

The problem can be stated simply as:
:$\min\limits_\;\; f(x)$

:$\mbox\$

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

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).

Methods for solving the problem

Examples

See also

* optimization
* Semi-Infinite Programming (SIP)

References

{{Reflist

External links

Mathematical Programming Glossary

Optimization in vector spaces