Semi-infinite programming
In optimization theory, semi-infinite programming is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a finite number of constraints. In the former case the constraints are typically parameterized.
Mathematical formulation of the problem
The problem can be stated simply as:where
SIP can be seen as a special case of bilevel programs in which the lower-level variables do not participate in the objective function.