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 problem, the feasible set of the parameters depends on the variables.

Mathematical formulation of the problem

The problem can be stated simply as:
where
In the special case that the set : is nonempty for all GSIP can be cast as bilevel programs.