Suvarna Garge (Editor)

Generalized semi infinite programming

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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 ∈ X f ( x ) subject to:   

where

f : R n → R g : R n × R m → R X ⊆ R n Y ⊆ R m .

In the special case that the set : Y ( x ) is nonempty for all x ∈ X GSIP can be cast as bilevel programs (Multilevel programming).

References

Generalized semi-infinite programming Wikipedia
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