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, [https://pdfs.semanticscholar.org/ce4f/c65e0dddd2c24580f0f3e05f5bf9b42ad723.pdf 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:

: $\min\limits_{x \in X}\;\; f(x)$

: $\mbox{subject to: }\$

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

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

References

External links

[http://glossary.computing.society.informs.org/ Mathematical Programming Glossary] {{Webarchive|url=https://web.archive.org/web/20100328165516/http://glossary.computing.society.informs.org/ |date=2010-03-28 }}

Category:Optimization in vector spaces