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.
[1] The problem can be stated simply as: where In the special case that the set :
GSIP can be cast as bilevel programs (Multilevel programming).