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 (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\in X}\;\;f(x)

\mbox{subject to: }\

g(x,y)\leq 0,\;\;\forall y\in Y(x)

where

f: R^n \to R

g: R^n \times 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).

References

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

External links

Mathematical Programming Glossary

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Generalized semi-infinite programming

Mathematical formulation of the problem

See also

References

External links