Generalized semi-infinite programming

In mathematics, generalized semi-infinite programming (GSIP) is an optimization problem with a finite number of variables and an infinite number of constraints. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The constraints are parameterized by parameters and the feasible set of the parameters depends on the variables.

1 Mathematical formulation of the problem
2 Methods for solving the problem
3 Examples
4 See also
5 References
6 External links

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). The "level" refers to sets of variables A bilevel program has two sets min f(x y x in X y in Y h(x y=0 g(x y=0

Methods for solving the problem

Examples

References

External links

Mathematical Programming Glossary

In Mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents

Mathematical formulation of the problem

Methods for solving the problem

Examples

See also

References

External links