Generalized semi-infinite programming explained

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]

Mathematical formulation of the problem

The problem can be stated simply as:

min \limits _{x} f(x) subjectto: g(x,y) \le 0 , \forall y \in Y(x)

where

f: R ^{n} \to R g: R ^{n} x 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).

See also

• optimization
• Semi-Infinite Programming (SIP)

External links

• Mathematical Programming Glossary

Notes and References

1. O. Stein and G. Still, On generalized semi-infinite optimization and bilevel optimization, European J. Oper. Res., 142 (2002), pp. 444-462